diff --git a/doc/source/whatsnew/v1.4.1.rst b/doc/source/whatsnew/v1.4.1.rst
index 19d8a2a9302d7..4536c06eb0867 100644
--- a/doc/source/whatsnew/v1.4.1.rst
+++ b/doc/source/whatsnew/v1.4.1.rst
@@ -36,6 +36,7 @@ Bug fixes
 - Stopped emitting unnecessary ``FutureWarning`` in :meth:`DataFrame.sort_values` with sparse columns (:issue:`45618`)
 - Fixed window aggregations in :meth:`DataFrame.rolling` and :meth:`Series.rolling` to skip over unused elements (:issue:`45647`)
 - Fixed builtin highlighters in :class:`.Styler` to be responsive to ``NA`` with nullable dtypes (:issue:`45804`)
+- Bug in :meth:`~Rolling.apply` with ``axis=1`` raising an erroneous ``ValueError`` (:issue:`45912`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index bbd0181e47401..72ebbcbc65e5e 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -1343,7 +1343,8 @@ def _generate_cython_apply_func(
 
         def apply_func(values, begin, end, min_periods, raw=raw):
             if not raw:
-                values = Series(values, index=self.obj.index)
+                # GH 45912
+                values = Series(values, index=self._on)
             return window_func(values, begin, end, min_periods)
 
         return apply_func
diff --git a/pandas/tests/window/test_apply.py b/pandas/tests/window/test_apply.py
index 8e690a677aa98..6683137960146 100644
--- a/pandas/tests/window/test_apply.py
+++ b/pandas/tests/window/test_apply.py
@@ -308,3 +308,11 @@ def test_center_reindex_frame(raw, frame):
     )
     frame_rs = frame.rolling(window=25, min_periods=minp, center=True).apply(f, raw=raw)
     tm.assert_frame_equal(frame_xp, frame_rs)
+
+
+def test_axis1(raw):
+    # GH 45912
+    df = DataFrame([1, 2])
+    result = df.rolling(window=1, axis=1).apply(np.sum, raw=raw)
+    expected = DataFrame([1.0, 2.0])
+    tm.assert_frame_equal(result, expected)