diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 722d0dcc10041..9f53ca404bd99 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -391,6 +391,7 @@ Datetimelike
 - :func:`to_datetime` would silently swap ``MM/DD/YYYY`` and ``DD/MM/YYYY`` formats if the given ``dayfirst`` option could not be respected - now, a warning is raised in the case of delimited date strings (e.g. ``31-12-2012``) (:issue:`12585`)
 - Bug in :meth:`date_range` and :meth:`bdate_range` do not return right bound when ``start`` = ``end`` and set is closed on one side (:issue:`43394`)
 - Bug in inplace addition and subtraction of :class:`DatetimeIndex` or :class:`TimedeltaIndex` with :class:`DatetimeArray` or :class:`TimedeltaArray` (:issue:`43904`)
+- Bug in in calling ``np.isnan``, ``np.isfinite``, or ``np.isinf`` on a timezone-aware :class:`DatetimeIndex` incorrectly raising ``TypeError`` (:issue:`43917`)
 -
 
 Timedelta
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 1f42463cb9f2d..420a409529a10 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1703,6 +1703,17 @@ class TimelikeOps(DatetimeLikeArrayMixin):
     Common ops for TimedeltaIndex/DatetimeIndex, but not PeriodIndex.
     """
 
+    def __array_ufunc__(self, ufunc: np.ufunc, method: str, *inputs, **kwargs):
+        if (
+            ufunc in [np.isnan, np.isinf, np.isfinite]
+            and len(inputs) == 1
+            and inputs[0] is self
+        ):
+            # numpy 1.18 changed isinf and isnan to not raise on dt64/td64
+            return getattr(ufunc, method)(self._ndarray, **kwargs)
+
+        return super().__array_ufunc__(ufunc, method, *inputs, **kwargs)
+
     def _round(self, freq, mode, ambiguous, nonexistent):
         # round the local times
         if is_datetime64tz_dtype(self.dtype):
diff --git a/pandas/tests/indexes/test_numpy_compat.py b/pandas/tests/indexes/test_numpy_compat.py
index 9cc1205310ea7..93b51cf9611f9 100644
--- a/pandas/tests/indexes/test_numpy_compat.py
+++ b/pandas/tests/indexes/test_numpy_compat.py
@@ -74,13 +74,6 @@ def test_numpy_ufuncs_other(index, func, request):
     # test ufuncs of numpy, see:
     # https://numpy.org/doc/stable/reference/ufuncs.html
     if isinstance(index, (DatetimeIndex, TimedeltaIndex)):
-        if (
-            isinstance(index, DatetimeIndex)
-            and index.tz is not None
-            and func in [np.isfinite, np.isnan, np.isinf]
-        ):
-            mark = pytest.mark.xfail(reason="__array_ufunc__ is not defined")
-            request.node.add_marker(mark)
 
         if func in (np.isfinite, np.isinf, np.isnan):
             # numpy 1.18 changed isinf and isnan to not raise on dt64/td64