diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index d00a418af3ddb..69eca8d8c175d 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -29,6 +29,7 @@ Fixed regressions
 - Fixed regression in :meth:`read_csv` in which the ``encoding`` option was not recognized with certain file-like objects (:issue:`31819`)
 - Fixed regression in :meth:`DataFrame.reindex` and :meth:`Series.reindex` when reindexing with (tz-aware) index and ``method=nearest`` (:issue:`26683`)
 - Fixed regression in :meth:`DataFrame.reindex_like` on a :class:`DataFrame` subclass raised an  ``AssertionError`` (:issue:`31925`)
+- Fixed regression in :meth:`Series.shift` with ``datetime64`` dtype when passing an integer ``fill_value`` (:issue:`32591`)
 
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index ec954e5721f1d..3d39d85158ffb 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -725,6 +725,57 @@ def _from_factorized(cls, values, original):
     def _values_for_argsort(self):
         return self._data
 
+    @Appender(ExtensionArray.shift.__doc__)
+    def shift(self, periods=1, fill_value=None, axis=0):
+        if not self.size or periods == 0:
+            return self.copy()
+
+        if is_valid_nat_for_dtype(fill_value, self.dtype):
+            fill_value = NaT
+        elif not isinstance(fill_value, self._recognized_scalars):
+            # only warn if we're not going to raise
+            if self._scalar_type is Period and lib.is_integer(fill_value):
+                # kludge for #31971 since Period(integer) tries to cast to str
+                new_fill = Period._from_ordinal(fill_value, freq=self.freq)
+            else:
+                new_fill = self._scalar_type(fill_value)
+
+            # stacklevel here is chosen to be correct when called from
+            #  DataFrame.shift or Series.shift
+            warnings.warn(
+                f"Passing {type(fill_value)} to shift is deprecated and "
+                "will raise in a future version, pass "
+                f"{self._scalar_type.__name__} instead.",
+                FutureWarning,
+                stacklevel=7,
+            )
+            fill_value = new_fill
+
+        fill_value = self._unbox_scalar(fill_value)
+
+        new_values = self._data
+
+        # make sure array sent to np.roll is c_contiguous
+        f_ordered = new_values.flags.f_contiguous
+        if f_ordered:
+            new_values = new_values.T
+            axis = new_values.ndim - axis - 1
+
+        new_values = np.roll(new_values, periods, axis=axis)
+
+        axis_indexer = [slice(None)] * self.ndim
+        if periods > 0:
+            axis_indexer[axis] = slice(None, periods)
+        else:
+            axis_indexer[axis] = slice(periods, None)
+        new_values[tuple(axis_indexer)] = fill_value
+
+        # restore original order
+        if f_ordered:
+            new_values = new_values.T
+
+        return type(self)._simple_new(new_values, dtype=self.dtype)
+
     # ------------------------------------------------------------------
     # Additional array methods
     #  These are not part of the EA API, but we implement them because
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 1229f2ad061b8..db98ec5ad388e 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1897,10 +1897,7 @@ def diff(self, n: int, axis: int = 1) -> List["Block"]:
         return super().diff(n, axis)
 
     def shift(
-        self,
-        periods: int,
-        axis: libinternals.BlockPlacement = 0,
-        fill_value: Any = None,
+        self, periods: int, axis: int = 0, fill_value: Any = None,
     ) -> List["ExtensionBlock"]:
         """
         Shift the block by `periods`.
@@ -2150,7 +2147,7 @@ def get_values(self, dtype=None):
 
     def iget(self, key):
         # GH#31649 we need to wrap scalars in Timestamp/Timedelta
-        # TODO: this can be removed if we ever have 2D EA
+        # TODO(EA2D): this can be removed if we ever have 2D EA
         result = super().iget(key)
         if isinstance(result, np.datetime64):
             result = Timestamp(result)
@@ -2158,6 +2155,12 @@ def iget(self, key):
             result = Timedelta(result)
         return result
 
+    def shift(self, periods, axis=0, fill_value=None):
+        # TODO(EA2D) this is unnecessary if these blocks are backed by 2D EAs
+        values = self.array_values()
+        new_values = values.shift(periods, fill_value=fill_value, axis=axis)
+        return self.make_block_same_class(new_values)
+
 
 class DatetimeBlock(DatetimeLikeBlockMixin, Block):
     __slots__ = ()
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index fa45db93c6102..3732818c0efc9 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -239,6 +239,23 @@ def test_inplace_arithmetic(self):
         arr -= pd.Timedelta(days=1)
         tm.assert_equal(arr, expected)
 
+    def test_shift_fill_int_deprecated(self):
+        # GH#31971
+        data = np.arange(10, dtype="i8") * 24 * 3600 * 10 ** 9
+        arr = self.array_cls(data, freq="D")
+
+        with tm.assert_produces_warning(FutureWarning, check_stacklevel=False):
+            result = arr.shift(1, fill_value=1)
+
+        expected = arr.copy()
+        if self.array_cls is PeriodArray:
+            fill_val = PeriodArray._scalar_type._from_ordinal(1, freq=arr.freq)
+        else:
+            fill_val = arr._scalar_type(1)
+        expected[0] = fill_val
+        expected[1:] = arr[:-1]
+        tm.assert_equal(result, expected)
+
 
 class TestDatetimeArray(SharedTests):
     index_cls = pd.DatetimeIndex
diff --git a/pandas/tests/frame/methods/test_shift.py b/pandas/tests/frame/methods/test_shift.py
index cfb17de892b1c..f6c89172bbf86 100644
--- a/pandas/tests/frame/methods/test_shift.py
+++ b/pandas/tests/frame/methods/test_shift.py
@@ -185,3 +185,26 @@ def test_tshift(self, datetime_frame):
         msg = "Freq was not given and was not set in the index"
         with pytest.raises(ValueError, match=msg):
             no_freq.tshift()
+
+    def test_shift_dt64values_int_fill_deprecated(self):
+        # GH#31971
+        ser = pd.Series([pd.Timestamp("2020-01-01"), pd.Timestamp("2020-01-02")])
+        df = ser.to_frame()
+
+        with tm.assert_produces_warning(FutureWarning):
+            result = df.shift(1, fill_value=0)
+
+        expected = pd.Series([pd.Timestamp(0), ser[0]]).to_frame()
+        tm.assert_frame_equal(result, expected)
+
+        # axis = 1
+        df2 = pd.DataFrame({"A": ser, "B": ser})
+        df2._consolidate_inplace()
+
+        with tm.assert_produces_warning(FutureWarning):
+            result = df2.shift(1, axis=1, fill_value=0)
+
+        expected = pd.DataFrame(
+            {"A": [pd.Timestamp(0), pd.Timestamp(0)], "B": df2["A"]}
+        )
+        tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_shift.py b/pandas/tests/series/methods/test_shift.py
index 8256e2f33b936..e8d7f5958d0a1 100644
--- a/pandas/tests/series/methods/test_shift.py
+++ b/pandas/tests/series/methods/test_shift.py
@@ -263,3 +263,13 @@ def test_shift_categorical(self):
 
         tm.assert_index_equal(s.values.categories, sp1.values.categories)
         tm.assert_index_equal(s.values.categories, sn2.values.categories)
+
+    def test_shift_dt64values_int_fill_deprecated(self):
+        # GH#31971
+        ser = pd.Series([pd.Timestamp("2020-01-01"), pd.Timestamp("2020-01-02")])
+
+        with tm.assert_produces_warning(FutureWarning):
+            result = ser.shift(1, fill_value=0)
+
+        expected = pd.Series([pd.Timestamp(0), ser[0]])
+        tm.assert_series_equal(result, expected)