diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 4c3e53ddcfa26..95825c814d57e 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -749,6 +749,7 @@ Numeric
 - Bug in :class:`DataFrame` arithmetic ops with a subclass whose :meth:`_constructor` attribute is a callable other than the subclass itself (:issue:`43201`)
 - Bug in arithmetic operations involving :class:`RangeIndex` where the result would have the incorrect ``name`` (:issue:`43962`)
 - Bug in arithmetic operations involving :class:`Series` where the result could have the incorrect ``name`` when the operands having matching NA or matching tuple names (:issue:`44459`)
+- Bug in :meth:`Series.clip` raising if bounds are a :class:`Series` with ``NA`` values for datetimes or nullable integer dtypes (:issue:`44785`)
 - Bug in division with ``IntegerDtype`` or ``BooleanDtype`` array and NA scalar incorrectly raising (:issue:`44685`)
 - Bug in multiplying a :class:`Series` with ``FloatingDtype`` with a timedelta-like scalar incorrectly raising (:issue:`44772`)
 -
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 1e25b0f4eb176..ba69847c55814 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -7381,7 +7381,14 @@ def _clip_with_one_bound(self, threshold, method, axis, inplace):
         # GH 40420
         # Treat missing thresholds as no bounds, not clipping the values
         if is_list_like(threshold):
-            fill_value = np.inf if method.__name__ == "le" else -np.inf
+            method_name_le = method.__name__ == "le"
+            if self.ndim == 1 and (
+                is_extension_array_dtype(self.dtype)
+                or is_datetime64_any_dtype(self.dtype)
+            ):
+                fill_value = self.max() if method_name_le else self.min()
+            else:
+                fill_value = np.inf if method_name_le else -np.inf
             threshold_inf = threshold.fillna(fill_value)
         else:
             threshold_inf = threshold
diff --git a/pandas/tests/series/methods/test_clip.py b/pandas/tests/series/methods/test_clip.py
index bc6d5aeb0a581..8a1f1bdaea091 100644
--- a/pandas/tests/series/methods/test_clip.py
+++ b/pandas/tests/series/methods/test_clip.py
@@ -89,6 +89,15 @@ def test_clip_against_series(self):
         tm.assert_series_equal(s.clip(lower, upper), Series([1.0, 2.0, 3.5]))
         tm.assert_series_equal(s.clip(1.5, upper), Series([1.5, 1.5, 3.5]))
 
+    @pytest.mark.parametrize("bound_values", [[pd.NA, 1], [1, pd.NA]])
+    def test_clip_against_series_ea_int_dtype(self, any_int_ea_dtype, bound_values):
+        # GH#44785
+        ser = Series([1, 1], dtype=any_int_ea_dtype)
+        bounds = Series(bound_values, dtype=any_int_ea_dtype)
+        expected = ser.copy()
+        result = ser.clip(bounds)
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize("inplace", [True, False])
     @pytest.mark.parametrize("upper", [[1, 2, 3], np.asarray([1, 2, 3])])
     def test_clip_against_list_like(self, inplace, upper):
@@ -138,6 +147,19 @@ def test_clip_with_timestamps_and_oob_datetimes(self):
 
         tm.assert_series_equal(result, expected)
 
+    def test_clip_timestamp_and_na(self, tz_naive_fixture):
+        # GH#44785
+        ser = Series([Timestamp("1970-01-01", tz=tz_naive_fixture)] * 2)
+        expected = ser.copy()
+
+        bounds = Series([pd.NaT, Timestamp("1970-01-01", tz=tz_naive_fixture)])
+        result = ser.clip(bounds)
+        tm.assert_series_equal(result, expected)
+
+        bounds = Series([Timestamp("1970-01-01", tz=tz_naive_fixture), pd.NaT])
+        result = ser.clip(bounds)
+        tm.assert_series_equal(result, expected)
+
     def test_clip_pos_args_deprecation(self):
         # https://github.com/pandas-dev/pandas/issues/41485
         ser = Series([1, 2, 3])