diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index f61721a0e51e6..dc1e8d359af55 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -190,13 +190,7 @@ def _engine_type(self):
     # Constructors
 
     def __new__(
-        cls,
-        data=None,
-        categories=None,
-        ordered=None,
-        dtype=None,
-        copy=False,
-        name=None,
+        cls, data=None, categories=None, ordered=None, dtype=None, copy=False, name=None
     ):
 
         dtype = CategoricalDtype._from_values_or_dtype(data, categories, ordered, dtype)
@@ -414,7 +408,7 @@ def astype(self, dtype, copy=True):
             if dtype == self.dtype:
                 return self.copy() if copy else self
 
-        return super().astype(dtype=dtype, copy=copy)
+        return Index.astype(self, dtype=dtype, copy=copy)
 
     @cache_readonly
     def _isnan(self):
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index a10e0f63b841d..6abd7d52d4071 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -542,18 +542,6 @@ def _concat_same_dtype(self, to_concat, name):
 
         return self._simple_new(new_data, **attribs)
 
-    @Appender(_index_shared_docs["astype"])
-    def astype(self, dtype, copy=True):
-        if is_dtype_equal(self.dtype, dtype) and copy is False:
-            # Ensure that self.astype(self.dtype) is self
-            return self
-
-        new_values = self._data.astype(dtype, copy=copy)
-
-        # pass copy=False because any copying will be done in the
-        #  _data.astype call above
-        return Index(new_values, dtype=new_values.dtype, name=self.name, copy=False)
-
     def shift(self, periods=1, freq=None):
         """
         Shift index by desired number of time frequency increments.
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index f0f407e9e8308..bb8b0343a3e2c 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -6,7 +6,7 @@
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import cache_readonly
 
-from pandas.core.dtypes.common import ensure_platform_int
+from pandas.core.dtypes.common import ensure_platform_int, is_dtype_equal
 from pandas.core.dtypes.generic import ABCSeries
 
 from pandas.core.arrays import ExtensionArray
@@ -192,3 +192,14 @@ def _get_unique_index(self, dropna=False):
         if dropna and self.hasnans:
             result = result[~result.isna()]
         return self._shallow_copy(result)
+
+    def astype(self, dtype, copy=True):
+        if is_dtype_equal(self.dtype, dtype) and copy is False:
+            # Ensure that self.astype(self.dtype) is self
+            return self
+
+        new_values = self._data.astype(dtype, copy=copy)
+
+        # pass copy=False because any copying will be done in the
+        #  _data.astype call above
+        return Index(new_values, dtype=new_values.dtype, name=self.name, copy=False)
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 6cf577f498162..24e3289d37c41 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -426,7 +426,7 @@ def astype(self, dtype, copy=True):
             new_values = self.values.astype(dtype, copy=copy)
         if is_interval_dtype(new_values):
             return self._shallow_copy(new_values.left, new_values.right)
-        return super().astype(dtype, copy=copy)
+        return Index.astype(self, dtype, copy=copy)
 
     @property
     def inferred_type(self) -> str: