diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 873c1e7cd41cc..38f1d837d614b 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -643,6 +643,7 @@ Datetimelike
 - Bug in :attr:`is_year_start` where a DateTimeIndex constructed via a date_range with frequency 'MS' wouldn't have the correct year or quarter start attributes (:issue:`57377`)
 - Bug in :class:`DataFrame` raising ``ValueError`` when ``dtype`` is ``timedelta64`` and ``data`` is a list containing ``None`` (:issue:`60064`)
 - Bug in :class:`Timestamp` constructor failing to raise when ``tz=None`` is explicitly specified in conjunction with timezone-aware ``tzinfo`` or data (:issue:`48688`)
+- Bug in :class:`Timestamp` where :meth:`normalize` overflows at edge cases without raising an exception (:issue:`60583`)
 - Bug in :func:`date_range` where the last valid timestamp would sometimes not be produced (:issue:`56134`)
 - Bug in :func:`date_range` where using a negative frequency value would not include all points between the start and end values (:issue:`56147`)
 - Bug in :func:`tseries.api.guess_datetime_format` would fail to infer time format when "%Y" == "%H%M" (:issue:`57452`)
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 452ba0fe869ee..78822804e4ec1 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -1269,7 +1269,7 @@ cdef class _Timestamp(ABCTimestamp):
             int64_t ppd = periods_per_day(self._creso)
             _Timestamp ts
 
-        normalized = normalize_i8_stamp(local_val, ppd)
+        normalized = normalize_i8_stamp(self, local_val, ppd)
         ts = type(self)._from_value_and_reso(normalized, reso=self._creso, tz=None)
         return ts.tz_localize(self.tzinfo)
 
@@ -3438,9 +3438,9 @@ Timestamp.daysinmonth = Timestamp.days_in_month
 # ----------------------------------------------------------------------
 # Scalar analogues to functions in vectorized.pyx
 
-
+@cython.overflowcheck(True)
 @cython.cdivision(False)
-cdef int64_t normalize_i8_stamp(int64_t local_val, int64_t ppd) noexcept nogil:
+cdef normalize_i8_stamp(self, int64_t local_val, int64_t ppd):
     """
     Round the localized nanosecond timestamp down to the previous midnight.
 
@@ -3454,4 +3454,15 @@ cdef int64_t normalize_i8_stamp(int64_t local_val, int64_t ppd) noexcept nogil:
     -------
     int64_t
     """
-    return local_val - (local_val % ppd)
+    cdef:
+        int64_t remainder
+        int64_t result
+    try:
+        remainder = local_val % ppd
+        result = local_val - remainder
+    except (OverflowError, OutOfBoundsDatetime) as err:
+        raise OutOfBoundsDatetime(
+            f"Cannot normalize {self} to midnight without overflow"
+        ) from err
+
+    return result
diff --git a/pandas/tests/scalar/timestamp/methods/test_normalize.py b/pandas/tests/scalar/timestamp/methods/test_normalize.py
index 60f249c602bd6..1c371e87fd55d 100644
--- a/pandas/tests/scalar/timestamp/methods/test_normalize.py
+++ b/pandas/tests/scalar/timestamp/methods/test_normalize.py
@@ -2,6 +2,7 @@
 
 from pandas._libs.tslibs import Timestamp
 from pandas._libs.tslibs.dtypes import NpyDatetimeUnit
+from pandas._libs.tslibs.np_datetime import OutOfBoundsDatetime
 
 
 class TestTimestampNormalize:
@@ -19,3 +20,16 @@ def test_normalize_pre_epoch_dates(self):
         result = Timestamp("1969-01-01 09:00:00").normalize()
         expected = Timestamp("1969-01-01 00:00:00")
         assert result == expected
+
+    def test_normalize_edge_cases(self):
+        # GH: 60583
+        expected_msg = (
+            r"Cannot normalize 1677-09-21 00:12:43\.145224193 to midnight "
+            "without overflow"
+        )
+        with pytest.raises(OutOfBoundsDatetime, match=expected_msg):
+            Timestamp.min.normalize()
+
+        result = Timestamp.max.normalize()
+        excepted = Timestamp("2262-04-11 00:00:00")
+        assert result == excepted