diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 9812521fe2767..cc8f26bf95a2f 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -390,6 +390,7 @@ Other
 ^^^^^
 - Bug in :class:`DataFrame` when passing a ``dict`` with a NA scalar and ``columns`` that would always return ``np.nan`` (:issue:`57205`)
 - Bug in :func:`tseries.api.guess_datetime_format` would fail to infer time format when "%Y" == "%H%M" (:issue:`57452`)
+- Bug in :func:`unique` on :class:`Index` not always returning :class:`Index` (:issue:`57043`)
 - Bug in :meth:`DataFrame.sort_index` when passing ``axis="columns"`` and ``ignore_index=True`` and ``ascending=False`` not returning a :class:`RangeIndex` columns (:issue:`57293`)
 - Bug in :meth:`DataFrame.where` where using a non-bool type array in the function would return a ``ValueError`` instead of a ``TypeError`` (:issue:`56330`)
 - Bug in Dataframe Interchange Protocol implementation was returning incorrect results for data buffers' associated dtype, for string and datetime columns (:issue:`54781`)
diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 774bbbe2463e9..344314d829c19 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -439,6 +439,10 @@ def unique_with_mask(values, mask: npt.NDArray[np.bool_] | None = None):
         # Dispatch to extension dtype's unique.
         return values.unique()
 
+    if isinstance(values, ABCIndex):
+        # Dispatch to Index's unique.
+        return values.unique()
+
     original = values
     hashtable, values = _get_hashtable_algo(values)
 
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index 057a5a627370e..365ec452a7f25 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -16,7 +16,10 @@
     is_integer_dtype,
     is_object_dtype,
 )
-from pandas.core.dtypes.dtypes import CategoricalDtype
+from pandas.core.dtypes.dtypes import (
+    CategoricalDtype,
+    DatetimeTZDtype,
+)
 
 import pandas as pd
 from pandas import (
@@ -570,19 +573,20 @@ def test_object_refcount_bug(self):
         for i in range(1000):
             len(algos.unique(lst))
 
-    def test_on_index_object(self):
-        mindex = MultiIndex.from_arrays(
-            [np.arange(5).repeat(5), np.tile(np.arange(5), 5)]
-        )
-        expected = mindex.values
-        expected.sort()
-
-        mindex = mindex.repeat(2)
+    def test_index_returned(self, index):
+        # GH#57043
+        index = index.repeat(2)
+        result = algos.unique(index)
 
-        result = pd.unique(mindex)
-        result.sort()
-
-        tm.assert_almost_equal(result, expected)
+        # dict.fromkeys preserves the order
+        unique_values = list(dict.fromkeys(index.values))
+        if isinstance(index, MultiIndex):
+            expected = MultiIndex.from_tuples(unique_values, names=index.names)
+        else:
+            expected = Index(unique_values, dtype=index.dtype)
+            if isinstance(index.dtype, DatetimeTZDtype):
+                expected = expected.normalize()
+        tm.assert_index_equal(result, expected, exact=True)
 
     def test_dtype_preservation(self, any_numpy_dtype):
         # GH 15442
@@ -623,7 +627,7 @@ def test_dtype_preservation(self, any_numpy_dtype):
 
     def test_datetime64_dtype_array_returned(self):
         # GH 9431
-        expected = np.array(
+        dt_arr = np.array(
             [
                 "2015-01-03T00:00:00.000000000",
                 "2015-01-01T00:00:00.000000000",
@@ -639,18 +643,18 @@ def test_datetime64_dtype_array_returned(self):
             ]
         )
         result = algos.unique(dt_index)
-        tm.assert_numpy_array_equal(result, expected)
-        assert result.dtype == expected.dtype
+        expected = to_datetime(dt_arr)
+        tm.assert_index_equal(result, expected, exact=True)
 
         s = Series(dt_index)
         result = algos.unique(s)
-        tm.assert_numpy_array_equal(result, expected)
-        assert result.dtype == expected.dtype
+        tm.assert_numpy_array_equal(result, dt_arr)
+        assert result.dtype == dt_arr.dtype
 
         arr = s.values
         result = algos.unique(arr)
-        tm.assert_numpy_array_equal(result, expected)
-        assert result.dtype == expected.dtype
+        tm.assert_numpy_array_equal(result, dt_arr)
+        assert result.dtype == dt_arr.dtype
 
     def test_datetime_non_ns(self):
         a = np.array(["2000", "2000", "2001"], dtype="datetime64[s]")
@@ -666,22 +670,23 @@ def test_timedelta_non_ns(self):
 
     def test_timedelta64_dtype_array_returned(self):
         # GH 9431
-        expected = np.array([31200, 45678, 10000], dtype="m8[ns]")
+        td_arr = np.array([31200, 45678, 10000], dtype="m8[ns]")
 
         td_index = to_timedelta([31200, 45678, 31200, 10000, 45678])
         result = algos.unique(td_index)
-        tm.assert_numpy_array_equal(result, expected)
+        expected = to_timedelta(td_arr)
+        tm.assert_index_equal(result, expected)
         assert result.dtype == expected.dtype
 
         s = Series(td_index)
         result = algos.unique(s)
-        tm.assert_numpy_array_equal(result, expected)
-        assert result.dtype == expected.dtype
+        tm.assert_numpy_array_equal(result, td_arr)
+        assert result.dtype == td_arr.dtype
 
         arr = s.values
         result = algos.unique(arr)
-        tm.assert_numpy_array_equal(result, expected)
-        assert result.dtype == expected.dtype
+        tm.assert_numpy_array_equal(result, td_arr)
+        assert result.dtype == td_arr.dtype
 
     def test_uint64_overflow(self):
         s = Series([1, 2, 2**63, 2**63], dtype=np.uint64)