diff --git a/doc/source/whatsnew/v1.0.1.rst b/doc/source/whatsnew/v1.0.1.rst
index be888f1952636..df8cf1932f793 100644
--- a/doc/source/whatsnew/v1.0.1.rst
+++ b/doc/source/whatsnew/v1.0.1.rst
@@ -22,6 +22,7 @@ Fixed regressions
 - Fixed regression in ``.groupby()`` aggregations with categorical dtype using Cythonized reduction functions (e.g. ``first``) (:issue:`31450`)
 - Fixed regression in :meth:`GroupBy.apply` if called with a function which returned a non-pandas non-scalar object (e.g. a list or numpy array) (:issue:`31441`)
 - Fixed regression in :meth:`DataFrame.groupby` whereby taking the minimum or maximum of a column with period dtype would raise a ``TypeError``. (:issue:`31471`)
+- Fixed regression in :meth:`DataFrame.apply` with object dtype and non-reducing function (:issue:`31505`)
 - Fixed regression in :meth:`to_datetime` when parsing non-nanosecond resolution datetimes (:issue:`31491`)
 - Fixed regression in :meth:`~DataFrame.to_csv` where specifying an ``na_rep`` might truncate the values written (:issue:`31447`)
 - Fixed regression in :class:`Categorical` construction with ``numpy.str_`` categories (:issue:`31499`)
diff --git a/pandas/_libs/reduction.pyx b/pandas/_libs/reduction.pyx
index 89164c527002a..43d253f632f0f 100644
--- a/pandas/_libs/reduction.pyx
+++ b/pandas/_libs/reduction.pyx
@@ -114,7 +114,8 @@ cdef class Reducer:
                     if self.typ is not None:
                         # In this case, we also have self.index
                         name = labels[i]
-                        cached_typ = self.typ(chunk, index=self.index, name=name)
+                        cached_typ = self.typ(
+                            chunk, index=self.index, name=name, dtype=arr.dtype)
 
                 # use the cached_typ if possible
                 if cached_typ is not None:
diff --git a/pandas/tests/frame/test_apply.py b/pandas/tests/frame/test_apply.py
index e98f74e133ea9..fe6abef97acc4 100644
--- a/pandas/tests/frame/test_apply.py
+++ b/pandas/tests/frame/test_apply.py
@@ -703,6 +703,14 @@ def apply_list(row):
         )
         tm.assert_series_equal(result, expected)
 
+    def test_apply_noreduction_tzaware_object(self):
+        # https://github.com/pandas-dev/pandas/issues/31505
+        df = pd.DataFrame({"foo": [pd.Timestamp("2020", tz="UTC")]}, dtype="object")
+        result = df.apply(lambda x: x)
+        tm.assert_frame_equal(result, df)
+        result = df.apply(lambda x: x.copy())
+        tm.assert_frame_equal(result, df)
+
 
 class TestInferOutputShape:
     # the user has supplied an opaque UDF where