diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 4c85b3d5dc745..be31a78776970 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -191,6 +191,7 @@ Removal of prior version deprecations/changes
 - Removed argument ``tz`` from :meth:`Period.to_timestamp`, use ``obj.to_timestamp(...).tz_localize(tz)`` instead (:issue:`34522`)
 - Removed argument ``is_copy`` from :meth:`DataFrame.take` and :meth:`Series.take` (:issue:`30615`)
 - Removed argument ``kind`` from :meth:`Index.get_slice_bound`, :meth:`Index.slice_indexer` and :meth:`Index.slice_locs` (:issue:`41378`)
+- Disallow subclass-specific keywords (e.g. "freq", "tz", "names", "closed") in the :class:`Index` constructor (:issue:`38597`)
 - Removed argument ``inplace`` from :meth:`Categorical.remove_unused_categories` (:issue:`37918`)
 - Disallow passing non-round floats to :class:`Timestamp` with ``unit="M"`` or ``unit="Y"`` (:issue:`47266`)
 - Remove keywords ``convert_float`` and ``mangle_dupe_cols`` from :func:`read_excel` (:issue:`41176`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 2fe61623abfd5..36a66533018bd 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -152,10 +152,6 @@
     Categorical,
     ExtensionArray,
 )
-from pandas.core.arrays.datetimes import (
-    tz_to_dtype,
-    validate_tz_from_dtype,
-)
 from pandas.core.arrays.string_ import StringArray
 from pandas.core.base import (
     IndexOpsMixin,
@@ -241,11 +237,6 @@ def join(
     return cast(F, join)
 
 
-def disallow_kwargs(kwargs: dict[str, Any]) -> None:
-    if kwargs:
-        raise TypeError(f"Unexpected keyword arguments {repr(set(kwargs))}")
-
-
 def _new_Index(cls, d):
     """
     This is called upon unpickling, rather than the default which doesn't
@@ -437,18 +428,8 @@ def __new__(
         copy: bool = False,
         name=None,
         tupleize_cols: bool = True,
-        **kwargs,
     ) -> Index:
 
-        if kwargs:
-            warnings.warn(
-                "Passing keywords other than 'data', 'dtype', 'copy', 'name', "
-                "'tupleize_cols' is deprecated and will raise TypeError in a "
-                "future version.  Use the specific Index subclass directly instead.",
-                FutureWarning,
-                stacklevel=find_stack_level(),
-            )
-
         from pandas.core.arrays import PandasArray
         from pandas.core.indexes.range import RangeIndex
 
@@ -456,10 +437,6 @@ def __new__(
 
         if dtype is not None:
             dtype = pandas_dtype(dtype)
-        if "tz" in kwargs:
-            tz = kwargs.pop("tz")
-            validate_tz_from_dtype(dtype, tz)
-            dtype = tz_to_dtype(tz)
 
         if type(data) is PandasArray:
             # ensure users don't accidentally put a PandasArray in an index,
@@ -481,18 +458,17 @@ def __new__(
             # non-EA dtype indexes have special casting logic, so we punt here
             klass = cls._dtype_to_subclass(dtype)
             if klass is not Index:
-                return klass(data, dtype=dtype, copy=copy, name=name, **kwargs)
+                return klass(data, dtype=dtype, copy=copy, name=name)
 
             ea_cls = dtype.construct_array_type()
             data = ea_cls._from_sequence(data, dtype=dtype, copy=copy)
-            disallow_kwargs(kwargs)
             return Index._simple_new(data, name=name)
 
         elif is_ea_or_datetimelike_dtype(data_dtype):
             data_dtype = cast(DtypeObj, data_dtype)
             klass = cls._dtype_to_subclass(data_dtype)
             if klass is not Index:
-                result = klass(data, copy=copy, name=name, **kwargs)
+                result = klass(data, copy=copy, name=name)
                 if dtype is not None:
                     return result.astype(dtype, copy=False)
                 return result
@@ -500,7 +476,6 @@ def __new__(
                 # GH#45206
                 data = data.astype(dtype, copy=False)
 
-            disallow_kwargs(kwargs)
             data = extract_array(data, extract_numpy=True)
             return Index._simple_new(data, name=name)
 
@@ -542,18 +517,14 @@ def __new__(
                     )
                     dtype = arr.dtype
 
-                    if kwargs:
-                        return cls(arr, dtype, copy=copy, name=name, **kwargs)
-
             klass = cls._dtype_to_subclass(arr.dtype)
             arr = klass._ensure_array(arr, dtype, copy)
-            disallow_kwargs(kwargs)
             return klass._simple_new(arr, name)
 
         elif is_scalar(data):
             raise cls._raise_scalar_data_error(data)
         elif hasattr(data, "__array__"):
-            return Index(np.asarray(data), dtype=dtype, copy=copy, name=name, **kwargs)
+            return Index(np.asarray(data), dtype=dtype, copy=copy, name=name)
         else:
 
             if tupleize_cols and is_list_like(data):
@@ -566,9 +537,7 @@ def __new__(
                     # 10697
                     from pandas.core.indexes.multi import MultiIndex
 
-                    return MultiIndex.from_tuples(
-                        data, names=name or kwargs.get("names")
-                    )
+                    return MultiIndex.from_tuples(data, names=name)
             # other iterable of some kind
 
             subarr = com.asarray_tuplesafe(data, dtype=_dtype_obj)
@@ -578,7 +547,7 @@ def __new__(
                     subarr, cast_numeric_deprecated=False
                 )
                 dtype = subarr.dtype
-            return Index(subarr, dtype=dtype, copy=copy, name=name, **kwargs)
+            return Index(subarr, dtype=dtype, copy=copy, name=name)
 
     @classmethod
     def _ensure_array(cls, data, dtype, copy: bool):
@@ -7081,19 +7050,6 @@ def shape(self) -> Shape:
         # See GH#27775, GH#27384 for history/reasoning in how this is defined.
         return (len(self),)
 
-    @final
-    def _deprecated_arg(self, value, name: str_t, methodname: str_t) -> None:
-        """
-        Issue a FutureWarning if the arg/kwarg is not no_default.
-        """
-        if value is not no_default:
-            warnings.warn(
-                f"'{name}' argument in {methodname} is deprecated "
-                "and will be removed in a future version.  Do not pass it.",
-                FutureWarning,
-                stacklevel=find_stack_level(),
-            )
-
 
 def ensure_index_from_sequences(sequences, names=None) -> Index:
     """
@@ -7246,14 +7202,6 @@ def maybe_extract_name(name, obj, cls) -> Hashable:
     return name
 
 
-_cast_depr_msg = (
-    "In a future version, passing an object-dtype arraylike to pd.Index will "
-    "not infer numeric values to numeric dtype (matching the Series behavior). "
-    "To retain the old behavior, explicitly pass the desired dtype or use the "
-    "desired Index subclass"
-)
-
-
 def _maybe_cast_data_without_dtype(
     subarr: np.ndarray, cast_numeric_deprecated: bool = True
 ) -> ArrayLike:
diff --git a/pandas/tests/indexes/base_class/test_constructors.py b/pandas/tests/indexes/base_class/test_constructors.py
index df04502a01f99..cf8b7214f3b91 100644
--- a/pandas/tests/indexes/base_class/test_constructors.py
+++ b/pandas/tests/indexes/base_class/test_constructors.py
@@ -30,12 +30,6 @@ def test_construction_list_mixed_tuples(self, index_vals):
         assert isinstance(index, Index)
         assert not isinstance(index, MultiIndex)
 
-    def test_constructor_wrong_kwargs(self):
-        # GH #19348
-        with pytest.raises(TypeError, match="Unexpected keyword arguments {'foo'}"):
-            with tm.assert_produces_warning(FutureWarning):
-                Index([], foo="bar")
-
     def test_constructor_cast(self):
         msg = "could not convert string to float"
         with pytest.raises(ValueError, match=msg):
diff --git a/pandas/tests/indexes/categorical/test_constructors.py b/pandas/tests/indexes/categorical/test_constructors.py
index 98da8038401e7..def865e03ed7c 100644
--- a/pandas/tests/indexes/categorical/test_constructors.py
+++ b/pandas/tests/indexes/categorical/test_constructors.py
@@ -145,15 +145,5 @@ def test_construction_with_categorical_dtype(self):
         with pytest.raises(ValueError, match=msg):
             CategoricalIndex(data, categories=cats, dtype=dtype)
 
-        with pytest.raises(ValueError, match=msg):
-            with tm.assert_produces_warning(FutureWarning):
-                # passing subclass-specific kwargs to pd.Index
-                Index(data, categories=cats, dtype=dtype)
-
         with pytest.raises(ValueError, match=msg):
             CategoricalIndex(data, ordered=ordered, dtype=dtype)
-
-        with pytest.raises(ValueError, match=msg):
-            with tm.assert_produces_warning(FutureWarning):
-                # passing subclass-specific kwargs to pd.Index
-                Index(data, ordered=ordered, dtype=dtype)
diff --git a/pandas/tests/indexes/datetimes/test_constructors.py b/pandas/tests/indexes/datetimes/test_constructors.py
index 67f323c5afd81..0061cfd2b903f 100644
--- a/pandas/tests/indexes/datetimes/test_constructors.py
+++ b/pandas/tests/indexes/datetimes/test_constructors.py
@@ -409,17 +409,6 @@ def test_construction_index_with_mixed_timezones_with_NaT(self):
         assert isinstance(result, DatetimeIndex)
         assert result.tz is None
 
-        # all NaT with tz
-        with tm.assert_produces_warning(FutureWarning):
-            # subclass-specific kwargs to pd.Index
-            result = Index([pd.NaT, pd.NaT], tz="Asia/Tokyo", name="idx")
-        exp = DatetimeIndex([pd.NaT, pd.NaT], tz="Asia/Tokyo", name="idx")
-
-        tm.assert_index_equal(result, exp, exact=True)
-        assert isinstance(result, DatetimeIndex)
-        assert result.tz is not None
-        assert result.tz == exp.tz
-
     def test_construction_dti_with_mixed_timezones(self):
         # GH 11488 (not changed, added explicit tests)
 
@@ -497,22 +486,6 @@ def test_construction_dti_with_mixed_timezones(self):
                 name="idx",
             )
 
-        with pytest.raises(ValueError, match=msg):
-            # passing tz should results in DatetimeIndex, then mismatch raises
-            # TypeError
-            with tm.assert_produces_warning(FutureWarning):
-                # subclass-specific kwargs to pd.Index
-                Index(
-                    [
-                        pd.NaT,
-                        Timestamp("2011-01-01 10:00"),
-                        pd.NaT,
-                        Timestamp("2011-01-02 10:00", tz="US/Eastern"),
-                    ],
-                    tz="Asia/Tokyo",
-                    name="idx",
-                )
-
     def test_construction_base_constructor(self):
         arr = [Timestamp("2011-01-01"), pd.NaT, Timestamp("2011-01-03")]
         tm.assert_index_equal(Index(arr), DatetimeIndex(arr))
diff --git a/pandas/tests/indexes/interval/test_constructors.py b/pandas/tests/indexes/interval/test_constructors.py
index a71a8f9e34ea9..315578a5dbf50 100644
--- a/pandas/tests/indexes/interval/test_constructors.py
+++ b/pandas/tests/indexes/interval/test_constructors.py
@@ -38,7 +38,6 @@ class ConstructorTests:
     get_kwargs_from_breaks to the expected format.
     """
 
-    @pytest.mark.filterwarnings("ignore:Passing keywords other:FutureWarning")
     @pytest.mark.parametrize(
         "breaks",
         [
@@ -96,22 +95,16 @@ def test_constructor_dtype(self, constructor, breaks, subtype):
     )
     def test_constructor_pass_closed(self, constructor, breaks):
         # not passing closed to IntervalDtype, but to IntervalArray constructor
-        warn = None
-        if isinstance(constructor, partial) and constructor.func is Index:
-            # passing kwargs to Index is deprecated
-            warn = FutureWarning
-
         iv_dtype = IntervalDtype(breaks.dtype)
 
         result_kwargs = self.get_kwargs_from_breaks(breaks)
 
         for dtype in (iv_dtype, str(iv_dtype)):
-            with tm.assert_produces_warning(warn):
+            with tm.assert_produces_warning(None):
 
                 result = constructor(dtype=dtype, closed="left", **result_kwargs)
             assert result.dtype.closed == "left"
 
-    @pytest.mark.filterwarnings("ignore:Passing keywords other:FutureWarning")
     @pytest.mark.parametrize("breaks", [[np.nan] * 2, [np.nan] * 4, [np.nan] * 50])
     def test_constructor_nan(self, constructor, breaks, closed):
         # GH 18421
@@ -125,7 +118,6 @@ def test_constructor_nan(self, constructor, breaks, closed):
         assert result.dtype.subtype == expected_subtype
         tm.assert_numpy_array_equal(np.array(result), expected_values)
 
-    @pytest.mark.filterwarnings("ignore:Passing keywords other:FutureWarning")
     @pytest.mark.parametrize(
         "breaks",
         [
@@ -353,9 +345,14 @@ class TestClassConstructors(ConstructorTests):
         params=[IntervalIndex, partial(Index, dtype="interval")],
         ids=["IntervalIndex", "Index"],
     )
-    def constructor(self, request):
+    def klass(self, request):
+        # We use a separate fixture here to include Index.__new__ with dtype kwarg
         return request.param
 
+    @pytest.fixture
+    def constructor(self):
+        return IntervalIndex
+
     def get_kwargs_from_breaks(self, breaks, closed="right"):
         """
         converts intervals in breaks format to a dictionary of kwargs to
@@ -388,12 +385,12 @@ def test_constructor_string(self):
         # the interval of strings is already forbidden.
         pass
 
-    def test_constructor_errors(self, constructor):
+    def test_constructor_errors(self, klass):
         # mismatched closed within intervals with no constructor override
         ivs = [Interval(0, 1, closed="right"), Interval(2, 3, closed="left")]
         msg = "intervals must all be closed on the same side"
         with pytest.raises(ValueError, match=msg):
-            constructor(ivs)
+            klass(ivs)
 
         # scalar
         msg = (
@@ -401,14 +398,13 @@ def test_constructor_errors(self, constructor):
             "some kind, 5 was passed"
         )
         with pytest.raises(TypeError, match=msg):
-            constructor(5)
+            klass(5)
 
         # not an interval; dtype depends on 32bit/windows builds
         msg = "type <class 'numpy.int(32|64)'> with value 0 is not an interval"
         with pytest.raises(TypeError, match=msg):
-            constructor([0, 1])
+            klass([0, 1])
 
-    @pytest.mark.filterwarnings("ignore:Passing keywords other:FutureWarning")
     @pytest.mark.parametrize(
         "data, closed",
         [
diff --git a/pandas/tests/indexes/multi/test_equivalence.py b/pandas/tests/indexes/multi/test_equivalence.py
index 18ff73dcb2221..c51b9386d7ec6 100644
--- a/pandas/tests/indexes/multi/test_equivalence.py
+++ b/pandas/tests/indexes/multi/test_equivalence.py
@@ -191,18 +191,7 @@ def test_identical(idx):
     mi2 = mi2.set_names(["new1", "new2"])
     assert mi.identical(mi2)
 
-    with tm.assert_produces_warning(FutureWarning):
-        # subclass-specific keywords to pd.Index
-        mi3 = Index(mi.tolist(), names=mi.names)
-
-    msg = r"Unexpected keyword arguments {'names'}"
-    with pytest.raises(TypeError, match=msg):
-        with tm.assert_produces_warning(FutureWarning):
-            # subclass-specific keywords to pd.Index
-            Index(mi.tolist(), names=mi.names, tupleize_cols=False)
-
     mi4 = Index(mi.tolist(), tupleize_cols=False)
-    assert mi.identical(mi3)
     assert not mi.identical(mi4)
     assert mi.equals(mi4)
 
diff --git a/pandas/tests/indexes/multi/test_names.py b/pandas/tests/indexes/multi/test_names.py
index cfbc90d1b36bb..5e3a427bc75ba 100644
--- a/pandas/tests/indexes/multi/test_names.py
+++ b/pandas/tests/indexes/multi/test_names.py
@@ -56,9 +56,7 @@ def test_take_preserve_name(idx):
 def test_copy_names():
     # Check that adding a "names" parameter to the copy is honored
     # GH14302
-    with tm.assert_produces_warning(FutureWarning):
-        # subclass-specific kwargs to pd.Index
-        multi_idx = pd.Index([(1, 2), (3, 4)], names=["MyName1", "MyName2"])
+    multi_idx = MultiIndex.from_tuples([(1, 2), (3, 4)], names=["MyName1", "MyName2"])
     multi_idx1 = multi_idx.copy()
 
     assert multi_idx.equals(multi_idx1)
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index bfe462cdf6c15..e5cce91b09a2f 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -250,9 +250,13 @@ def test_constructor_dtypes_datetime(self, tz_naive_fixture, attr, klass):
 
         if attr == "asi8":
             result = DatetimeIndex(arg).tz_localize(tz_naive_fixture)
+            tm.assert_index_equal(result, index)
+        elif klass is Index:
+            with pytest.raises(TypeError, match="unexpected keyword"):
+                klass(arg, tz=tz_naive_fixture)
         else:
             result = klass(arg, tz=tz_naive_fixture)
-        tm.assert_index_equal(result, index)
+            tm.assert_index_equal(result, index)
 
         if attr == "asi8":
             if err:
@@ -267,9 +271,13 @@ def test_constructor_dtypes_datetime(self, tz_naive_fixture, attr, klass):
 
         if attr == "asi8":
             result = DatetimeIndex(list(arg)).tz_localize(tz_naive_fixture)
+            tm.assert_index_equal(result, index)
+        elif klass is Index:
+            with pytest.raises(TypeError, match="unexpected keyword"):
+                klass(arg, tz=tz_naive_fixture)
         else:
             result = klass(list(arg), tz=tz_naive_fixture)
-        tm.assert_index_equal(result, index)
+            tm.assert_index_equal(result, index)
 
         if attr == "asi8":
             if err:
diff --git a/pandas/tests/indexing/test_coercion.py b/pandas/tests/indexing/test_coercion.py
index 2d54a9ba370ca..26424904482d1 100644
--- a/pandas/tests/indexing/test_coercion.py
+++ b/pandas/tests/indexing/test_coercion.py
@@ -368,12 +368,6 @@ def test_insert_index_period(self, insert, coerced_val, coerced_dtype):
                 expected = obj.astype(object).insert(0, str(insert))
                 tm.assert_index_equal(result, expected)
 
-            msg = r"Unexpected keyword arguments {'freq'}"
-            with pytest.raises(TypeError, match=msg):
-                with tm.assert_produces_warning(FutureWarning):
-                    # passing keywords to pd.Index
-                    pd.Index(data, freq="M")
-
     @pytest.mark.xfail(reason="Test not implemented")
     def test_insert_index_complex128(self):
         raise NotImplementedError