diff --git a/doc/source/whatsnew/v1.1.3.rst b/doc/source/whatsnew/v1.1.3.rst
index c63a78c76572f..4ad85fd6bafa6 100644
--- a/doc/source/whatsnew/v1.1.3.rst
+++ b/doc/source/whatsnew/v1.1.3.rst
@@ -38,6 +38,7 @@ Fixed regressions
 - Fixed regression in :meth:`DataFrame.apply` with ``raw=True`` and user-function returning string (:issue:`35940`)
 - Fixed regression when setting empty :class:`DataFrame` column to a :class:`Series` in preserving name of index in frame (:issue:`36527`)
 - Fixed regression in :class:`Period` incorrect value for ordinal over the maximum timestamp (:issue:`36430`)
+- Fixed regression in :meth:`Series.dt.normalize` when normalizing pre-epoch dates the result was shifted one day (:issue:`36294`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index adf1dfbc1ac72..3b52b4d499694 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -830,7 +830,7 @@ cpdef inline datetime localize_pydatetime(datetime dt, object tz):
 # ----------------------------------------------------------------------
 # Normalization
 
-@cython.cdivision
+@cython.cdivision(False)
 cdef inline int64_t normalize_i8_stamp(int64_t local_val) nogil:
     """
     Round the localized nanosecond timestamp down to the previous midnight.
diff --git a/pandas/tests/scalar/timestamp/test_unary_ops.py b/pandas/tests/scalar/timestamp/test_unary_ops.py
index 8641bbd0a66f2..e8196cd8328e7 100644
--- a/pandas/tests/scalar/timestamp/test_unary_ops.py
+++ b/pandas/tests/scalar/timestamp/test_unary_ops.py
@@ -397,6 +397,12 @@ def test_normalize(self, tz_naive_fixture, arg):
         expected = Timestamp("2013-11-30", tz=tz)
         assert result == expected
 
+    def test_normalize_pre_epoch_dates(self):
+        # GH: 36294
+        result = Timestamp("1969-01-01 09:00:00").normalize()
+        expected = Timestamp("1969-01-01 00:00:00")
+        assert result == expected
+
     # --------------------------------------------------------------
 
     @td.skip_if_windows
diff --git a/pandas/tests/series/test_datetime_values.py b/pandas/tests/series/test_datetime_values.py
index 723bd303b1974..b0926089bd7b4 100644
--- a/pandas/tests/series/test_datetime_values.py
+++ b/pandas/tests/series/test_datetime_values.py
@@ -702,3 +702,11 @@ def test_week_and_weekofyear_are_deprecated():
         series.dt.week
     with tm.assert_produces_warning(FutureWarning):
         series.dt.weekofyear
+
+
+def test_normalize_pre_epoch_dates():
+    # GH: 36294
+    s = pd.to_datetime(pd.Series(["1969-01-01 09:00:00", "2016-01-01 09:00:00"]))
+    result = s.dt.normalize()
+    expected = pd.to_datetime(pd.Series(["1969-01-01", "2016-01-01"]))
+    tm.assert_series_equal(result, expected)