diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 0c40900d54b53..4697f2d2e59a4 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -831,20 +831,6 @@ def slice_indexer(self, start=None, end=None, step=None, kind=None):
             else:
                 raise
 
-    # --------------------------------------------------------------------
-    # Wrapping DatetimeArray
-
-    def __getitem__(self, key):
-        result = self._data.__getitem__(key)
-        if is_scalar(result):
-            return result
-        elif result.ndim > 1:
-            # To support MPL which performs slicing with 2 dim
-            # even though it only has 1 dim by definition
-            assert isinstance(result, np.ndarray), result
-            return result
-        return type(self)(result, name=self.name)
-
     # --------------------------------------------------------------------
 
     @Substitution(klass="DatetimeIndex")
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index 9011616dfe496..bd089f574a313 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -3,6 +3,8 @@
 """
 from typing import List
 
+import numpy as np
+
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import cache_readonly
 
@@ -170,6 +172,29 @@ class ExtensionIndex(Index):
     __le__ = _make_wrapped_comparison_op("__le__")
     __ge__ = _make_wrapped_comparison_op("__ge__")
 
+    def __getitem__(self, key):
+        result = self._data[key]
+        if isinstance(result, type(self._data)):
+            return type(self)(result, name=self.name)
+
+        # Includes cases where we get a 2D ndarray back for MPL compat
+        return result
+
+    def __iter__(self):
+        return self._data.__iter__()
+
+    @property
+    def _ndarray_values(self) -> np.ndarray:
+        return self._data._ndarray_values
+
+    def dropna(self, how="any"):
+        if how not in ("any", "all"):
+            raise ValueError(f"invalid how option: {how}")
+
+        if self.hasnans:
+            return self._shallow_copy(self._data[~self._isnan])
+        return self._shallow_copy()
+
     def repeat(self, repeats, axis=None):
         nv.validate_repeat(tuple(), dict(axis=axis))
         result = self._data.repeat(repeats, axis=axis)
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 86dd4525c7d6d..1f3182bc83e1d 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -211,15 +211,6 @@ def _formatter_func(self):
 
         return _get_format_timedelta64(self, box=True)
 
-    # -------------------------------------------------------------------
-    # Wrapping TimedeltaArray
-
-    def __getitem__(self, key):
-        result = self._data.__getitem__(key)
-        if is_scalar(result):
-            return result
-        return type(self)(result, name=self.name)
-
     # -------------------------------------------------------------------
 
     @Appender(_index_shared_docs["astype"])