diff --git a/doc/source/whatsnew/v2.0.3.rst b/doc/source/whatsnew/v2.0.3.rst
index 0f56f203a5802..160223168d83c 100644
--- a/doc/source/whatsnew/v2.0.3.rst
+++ b/doc/source/whatsnew/v2.0.3.rst
@@ -26,6 +26,7 @@ Bug fixes
 - Bug in :func:`read_csv` when defining ``dtype`` with ``bool[pyarrow]`` for the ``"c"`` and ``"python"`` engines (:issue:`53390`)
 - Bug in :meth:`Series.str.split` and :meth:`Series.str.rsplit` with ``expand=True`` for :class:`ArrowDtype` with ``pyarrow.string`` (:issue:`53532`)
 - Bug in indexing methods (e.g. :meth:`DataFrame.__getitem__`) where taking the entire :class:`DataFrame`/:class:`Series` would raise an ``OverflowError`` when Copy on Write was enabled and the length of the array was over the maximum size a 32-bit integer can hold (:issue:`53616`)
+- Bug when indexing a :class:`DataFrame` or :class:`Series` with an :class:`Index` with a timestamp :class:`ArrowDtype` would raise an ``AttributeError`` (:issue:`53644`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_203.other:
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 7f03819af6723..0e2ef1d63655d 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5880,7 +5880,9 @@ def _get_indexer_strict(self, key, axis_name: str_t) -> tuple[Index, np.ndarray]
         if isinstance(key, Index):
             # GH 42790 - Preserve name from an Index
             keyarr.name = key.name
-        if keyarr.dtype.kind in ["m", "M"]:
+        if (
+            isinstance(keyarr.dtype, np.dtype) and keyarr.dtype.kind in ["m", "M"]
+        ) or isinstance(keyarr.dtype, DatetimeTZDtype):
             # DTI/TDI.take can infer a freq in some cases when we dont want one
             if isinstance(key, list) or (
                 isinstance(key, type(self))
diff --git a/pandas/tests/indexing/test_datetime.py b/pandas/tests/indexing/test_datetime.py
index 15e1fae77d65b..6510612ba6f87 100644
--- a/pandas/tests/indexing/test_datetime.py
+++ b/pandas/tests/indexing/test_datetime.py
@@ -168,3 +168,21 @@ def test_getitem_str_slice_millisecond_resolution(self, frame_or_series):
             ],
         )
         tm.assert_equal(result, expected)
+
+    def test_getitem_pyarrow_index(self, frame_or_series):
+        # GH 53644
+        pytest.importorskip("pyarrow")
+        obj = frame_or_series(
+            range(5),
+            index=date_range("2020", freq="D", periods=5).astype(
+                "timestamp[us][pyarrow]"
+            ),
+        )
+        result = obj.loc[obj.index[:-3]]
+        expected = frame_or_series(
+            range(2),
+            index=date_range("2020", freq="D", periods=2).astype(
+                "timestamp[us][pyarrow]"
+            ),
+        )
+        tm.assert_equal(result, expected)