diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 2a50ebd959ace..68069a2e9482c 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -906,13 +906,10 @@ def astype(self, dtype, copy=True):
         if is_dtype_equal(self.dtype, dtype):
             return self.copy() if copy else self
 
-        elif is_categorical_dtype(dtype):
-            from pandas.core.indexes.category import CategoricalIndex
-
-            return CategoricalIndex(self, name=self.name, dtype=dtype, copy=copy)
-
-        elif is_extension_array_dtype(dtype):
-            return Index(np.asarray(self), name=self.name, dtype=dtype, copy=copy)
+        elif isinstance(dtype, ExtensionDtype):
+            cls = dtype.construct_array_type()
+            new_values = cls._from_sequence(self, dtype=dtype, copy=False)
+            return Index(new_values, dtype=dtype, copy=copy, name=self.name)
 
         try:
             casted = self._values.astype(dtype, copy=copy)
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index 83998a2792a8a..066fa1f547328 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -18,6 +18,7 @@
     cache_readonly,
     doc,
 )
+from pandas.util._exceptions import rewrite_exception
 
 from pandas.core.dtypes.cast import (
     find_common_type,
@@ -365,11 +366,17 @@ def astype(self, dtype, copy: bool = True) -> Index:
                 return self
             return self.copy()
 
-        if isinstance(dtype, np.dtype) and dtype.kind == "M" and dtype != "M8[ns]":
+        if (
+            isinstance(self.dtype, np.dtype)
+            and isinstance(dtype, np.dtype)
+            and dtype.kind == "M"
+            and dtype != "M8[ns]"
+        ):
             # For now Datetime supports this by unwrapping ndarray, but DTI doesn't
-            raise TypeError(f"Cannot cast {type(self._data).__name__} to dtype")
+            raise TypeError(f"Cannot cast {type(self).__name__} to dtype")
 
-        new_values = self._data.astype(dtype, copy=copy)
+        with rewrite_exception(type(self._data).__name__, type(self).__name__):
+            new_values = self._data.astype(dtype, copy=copy)
 
         # pass copy=False because any copying will be done in the
         #  _data.astype call above
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 894abb0fb1776..61f3d62320a6e 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -422,12 +422,6 @@ def __reduce__(self):
         d.update(self._get_attributes_dict())
         return _new_IntervalIndex, (type(self), d), None
 
-    @Appender(Index.astype.__doc__)
-    def astype(self, dtype, copy: bool = True):
-        with rewrite_exception("IntervalArray", type(self).__name__):
-            new_values = self._values.astype(dtype, copy=copy)
-        return Index(new_values, dtype=new_values.dtype, name=self.name)
-
     @property
     def inferred_type(self) -> str:
         """Return a string of the type inferred from the values"""
diff --git a/pandas/tests/indexes/datetimes/methods/test_astype.py b/pandas/tests/indexes/datetimes/methods/test_astype.py
index 24387267cd5c4..3e329818540c3 100644
--- a/pandas/tests/indexes/datetimes/methods/test_astype.py
+++ b/pandas/tests/indexes/datetimes/methods/test_astype.py
@@ -223,7 +223,7 @@ def test_astype_object_with_nat(self):
     def test_astype_raises(self, dtype):
         # GH 13149, GH 13209
         idx = DatetimeIndex(["2016-05-16", "NaT", NaT, np.NaN])
-        msg = "Cannot cast DatetimeArray to dtype"
+        msg = "Cannot cast DatetimeIndex to dtype"
         with pytest.raises(TypeError, match=msg):
             idx.astype(dtype)
 
diff --git a/pandas/tests/indexes/period/methods/test_astype.py b/pandas/tests/indexes/period/methods/test_astype.py
index 73439d349bebd..74f627478a29c 100644
--- a/pandas/tests/indexes/period/methods/test_astype.py
+++ b/pandas/tests/indexes/period/methods/test_astype.py
@@ -21,7 +21,7 @@ class TestPeriodIndexAsType:
     def test_astype_raises(self, dtype):
         # GH#13149, GH#13209
         idx = PeriodIndex(["2016-05-16", "NaT", NaT, np.NaN], freq="D")
-        msg = "Cannot cast PeriodArray to dtype"
+        msg = "Cannot cast PeriodIndex to dtype"
         with pytest.raises(TypeError, match=msg):
             idx.astype(dtype)
 
diff --git a/pandas/tests/indexes/period/test_constructors.py b/pandas/tests/indexes/period/test_constructors.py
index 54e61b35eb70f..e372fd007630a 100644
--- a/pandas/tests/indexes/period/test_constructors.py
+++ b/pandas/tests/indexes/period/test_constructors.py
@@ -538,7 +538,7 @@ def setup_method(self, method):
         self.series = Series(period_range("2000-01-01", periods=10, freq="D"))
 
     def test_constructor_cant_cast_period(self):
-        msg = "Cannot cast PeriodArray to dtype float64"
+        msg = "Cannot cast PeriodIndex to dtype float64"
         with pytest.raises(TypeError, match=msg):
             Series(period_range("2000-01-01", periods=10, freq="D"), dtype=float)
 
diff --git a/pandas/tests/indexes/timedeltas/methods/test_astype.py b/pandas/tests/indexes/timedeltas/methods/test_astype.py
index c2c7a1f32ae6e..fbe66bf78dbeb 100644
--- a/pandas/tests/indexes/timedeltas/methods/test_astype.py
+++ b/pandas/tests/indexes/timedeltas/methods/test_astype.py
@@ -101,7 +101,7 @@ def test_astype_timedelta64(self):
     def test_astype_raises(self, dtype):
         # GH 13149, GH 13209
         idx = TimedeltaIndex([1e14, "NaT", NaT, np.NaN])
-        msg = "Cannot cast TimedeltaArray to dtype"
+        msg = "Cannot cast TimedeltaIndex to dtype"
         with pytest.raises(TypeError, match=msg):
             idx.astype(dtype)