diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index fecfc956852e3..653082fa3b67a 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -753,6 +753,7 @@ Other
 - Bug in :meth:`Series.to_frame` and :meth:`Index.to_frame` ignoring the ``name`` argument when ``name=None`` is explicitly passed (:issue:`44212`)
 - Bug in :meth:`Series.replace` and :meth:`DataFrame.replace` with ``value=None`` and ExtensionDtypes (:issue:`44270`)
 - Bug in :meth:`FloatingArray.equals` failing to consider two arrays equal if they contain ``np.nan`` values (:issue:`44382`)
+- Bug in :meth:`DataFrame.shift` with ``axis=1`` and ``ExtensionDtype`` columns incorrectly raising when an incompatible ``fill_value`` is passed (:issue:`44564`)
 - Bug in :meth:`DataFrame.diff` when passing a NumPy integer object instead of an ``int`` object (:issue:`44572`)
 -
 
diff --git a/pandas/core/internals/managers.py b/pandas/core/internals/managers.py
index 74d785586b950..d69709bf9d06c 100644
--- a/pandas/core/internals/managers.py
+++ b/pandas/core/internals/managers.py
@@ -36,6 +36,7 @@
     is_1d_only_ea_dtype,
     is_dtype_equal,
     is_list_like,
+    needs_i8_conversion,
 )
 from pandas.core.dtypes.dtypes import ExtensionDtype
 from pandas.core.dtypes.generic import (
@@ -362,7 +363,28 @@ def shift(self: T, periods: int, axis: int, fill_value) -> T:
         if fill_value is lib.no_default:
             fill_value = None
 
-        if axis == 0 and self.ndim == 2 and self.nblocks > 1:
+        if (
+            axis == 0
+            and self.ndim == 2
+            and (
+                self.nblocks > 1
+                or (
+                    # If we only have one block and we know that we can't
+                    #  keep the same dtype (i.e. the _can_hold_element check)
+                    #  then we can go through the reindex_indexer path
+                    #  (and avoid casting logic in the Block method).
+                    #  The exception to this (until 2.0) is datetimelike
+                    #  dtypes with integers, which cast.
+                    not self.blocks[0]._can_hold_element(fill_value)
+                    # TODO(2.0): remove special case for integer-with-datetimelike
+                    #  once deprecation is enforced
+                    and not (
+                        lib.is_integer(fill_value)
+                        and needs_i8_conversion(self.blocks[0].dtype)
+                    )
+                )
+            )
+        ):
             # GH#35488 we need to watch out for multi-block cases
             # We only get here with fill_value not-lib.no_default
             ncols = self.shape[0]
diff --git a/pandas/tests/frame/methods/test_shift.py b/pandas/tests/frame/methods/test_shift.py
index d8511581f0e94..9cd0b8bb5b315 100644
--- a/pandas/tests/frame/methods/test_shift.py
+++ b/pandas/tests/frame/methods/test_shift.py
@@ -331,6 +331,83 @@ def test_shift_dt64values_int_fill_deprecated(self):
         expected = DataFrame({"A": [pd.Timestamp(0), pd.Timestamp(0)], "B": df2["A"]})
         tm.assert_frame_equal(result, expected)
 
+        # same thing but not consolidated
+        # This isn't great that we get different behavior, but
+        #  that will go away when the deprecation is enforced
+        df3 = DataFrame({"A": ser})
+        df3["B"] = ser
+        assert len(df3._mgr.arrays) == 2
+        result = df3.shift(1, axis=1, fill_value=0)
+        expected = DataFrame({"A": [0, 0], "B": df2["A"]})
+        tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "as_cat",
+        [
+            pytest.param(
+                True,
+                marks=pytest.mark.xfail(
+                    reason="_can_hold_element incorrectly always returns True"
+                ),
+            ),
+            False,
+        ],
+    )
+    @pytest.mark.parametrize(
+        "vals",
+        [
+            date_range("2020-01-01", periods=2),
+            date_range("2020-01-01", periods=2, tz="US/Pacific"),
+            pd.period_range("2020-01-01", periods=2, freq="D"),
+            pd.timedelta_range("2020 Days", periods=2, freq="D"),
+            pd.interval_range(0, 3, periods=2),
+            pytest.param(
+                pd.array([1, 2], dtype="Int64"),
+                marks=pytest.mark.xfail(
+                    reason="_can_hold_element incorrectly always returns True"
+                ),
+            ),
+            pytest.param(
+                pd.array([1, 2], dtype="Float32"),
+                marks=pytest.mark.xfail(
+                    reason="_can_hold_element incorrectly always returns True"
+                ),
+            ),
+        ],
+        ids=lambda x: str(x.dtype),
+    )
+    def test_shift_dt64values_axis1_invalid_fill(
+        self, vals, as_cat, using_array_manager, request
+    ):
+        # GH#44564
+        if using_array_manager:
+            mark = pytest.mark.xfail(raises=NotImplementedError)
+            request.node.add_marker(mark)
+
+        ser = Series(vals)
+        if as_cat:
+            ser = ser.astype("category")
+
+        df = DataFrame({"A": ser})
+        result = df.shift(-1, axis=1, fill_value="foo")
+        expected = DataFrame({"A": ["foo", "foo"]})
+        tm.assert_frame_equal(result, expected)
+
+        # same thing but multiple blocks
+        df2 = DataFrame({"A": ser, "B": ser})
+        df2._consolidate_inplace()
+
+        result = df2.shift(-1, axis=1, fill_value="foo")
+        expected = DataFrame({"A": df2["B"], "B": ["foo", "foo"]})
+        tm.assert_frame_equal(result, expected)
+
+        # same thing but not consolidated
+        df3 = DataFrame({"A": ser})
+        df3["B"] = ser
+        assert len(df3._mgr.arrays) == 2
+        result = df3.shift(-1, axis=1, fill_value="foo")
+        tm.assert_frame_equal(result, expected)
+
     def test_shift_axis1_categorical_columns(self):
         # GH#38434
         ci = CategoricalIndex(["a", "b", "c"])