diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 6e475acc5d971..c49695f009fc8 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -902,6 +902,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.union` and :meth:`DatetimeIndex.intersection` when ``unit`` was non-nanosecond (:issue:`59036`)
 - Bug in :meth:`Index.union` with a ``pyarrow`` timestamp dtype incorrectly returning ``object`` dtype (:issue:`58421`)
 - Bug in :meth:`Series.dt.microsecond` producing incorrect results for pyarrow backed :class:`Series`. (:issue:`59154`)
+- Bug in :meth:`Timestamp.normalize` and :meth:`DatetimeArray.normalize` returning incorrect results instead of raising on integer overflow for very small (distant past) values (:issue:`60583`)
 - Bug in :meth:`Timestamp.replace` failing to update ``unit`` attribute when replacement introduces non-zero ``nanosecond`` or ``microsecond`` (:issue:`57749`)
 - Bug in :meth:`to_datetime` not respecting dayfirst if an uncommon date string was passed. (:issue:`58859`)
 - Bug in :meth:`to_datetime` on float array with missing values throwing ``FloatingPointError`` (:issue:`58419`)
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index df1ead215a2be..2f0c5fa9ef18e 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -1339,7 +1339,12 @@ cdef class _Timestamp(ABCTimestamp):
             int64_t ppd = periods_per_day(self._creso)
             _Timestamp ts
 
-        normalized = normalize_i8_stamp(local_val, ppd)
+        try:
+            normalized = normalize_i8_stamp(local_val, ppd)
+        except OverflowError as err:
+            raise ValueError(
+                "Cannot normalize Timestamp without integer overflow"
+            ) from err
         ts = type(self)._from_value_and_reso(normalized, reso=self._creso, tz=None)
         return ts.tz_localize(self.tzinfo)
 
@@ -3547,7 +3552,7 @@ Timestamp.daysinmonth = Timestamp.days_in_month
 
 
 @cython.cdivision(False)
-cdef int64_t normalize_i8_stamp(int64_t local_val, int64_t ppd) noexcept nogil:
+cdef int64_t normalize_i8_stamp(int64_t local_val, int64_t ppd):
     """
     Round the localized nanosecond timestamp down to the previous midnight.
 
@@ -3561,4 +3566,6 @@ cdef int64_t normalize_i8_stamp(int64_t local_val, int64_t ppd) noexcept nogil:
     -------
     int64_t
     """
-    return local_val - (local_val % ppd)
+    with cython.overflowcheck(True):
+        # GH#60583
+        return local_val - (local_val % ppd)
diff --git a/pandas/_libs/tslibs/vectorized.pyx b/pandas/_libs/tslibs/vectorized.pyx
index 1e09874639d4f..636104a1e0f1e 100644
--- a/pandas/_libs/tslibs/vectorized.pyx
+++ b/pandas/_libs/tslibs/vectorized.pyx
@@ -254,6 +254,7 @@ def get_resolution(
 # -------------------------------------------------------------------------
 
 
+@cython.overflowcheck(True)
 @cython.cdivision(False)
 @cython.wraparound(False)
 @cython.boundscheck(False)
@@ -292,8 +293,12 @@ cpdef ndarray normalize_i8_timestamps(ndarray stamps, tzinfo tz, NPY_DATETIMEUNI
             res_val = NPY_NAT
         else:
             local_val = info.utc_val_to_local_val(utc_val, &pos)
-            res_val = local_val - (local_val % ppd)
-
+            try:
+                res_val = local_val - (local_val % ppd)
+            except OverflowError as err:
+                raise ValueError(
+                    "Cannot normalize Timestamp without integer overflow"
+                ) from err
         # Analogous to: result[i] = res_val
         (<int64_t*>cnp.PyArray_MultiIter_DATA(mi, 0))[0] = res_val
 
diff --git a/pandas/tests/arrays/test_datetimes.py b/pandas/tests/arrays/test_datetimes.py
index a2a2d57a33925..199e3572732a0 100644
--- a/pandas/tests/arrays/test_datetimes.py
+++ b/pandas/tests/arrays/test_datetimes.py
@@ -93,6 +93,15 @@ def test_normalize(self, unit):
         res = dta.normalize()
         tm.assert_extension_array_equal(res, expected)
 
+    def test_normalize_overflow_raises(self):
+        # GH#60583
+        ts = pd.Timestamp.min
+        dta = DatetimeArray._from_sequence([ts], dtype="M8[ns]")
+
+        msg = "Cannot normalize Timestamp without integer overflow"
+        with pytest.raises(ValueError, match=msg):
+            dta.normalize()
+
     def test_simple_new_requires_match(self, unit):
         arr = np.arange(5, dtype=np.int64).view(f"M8[{unit}]")
         dtype = DatetimeTZDtype(unit, "UTC")
diff --git a/pandas/tests/scalar/timestamp/methods/test_normalize.py b/pandas/tests/scalar/timestamp/methods/test_normalize.py
index 60f249c602bd6..4e8a6e1bc7197 100644
--- a/pandas/tests/scalar/timestamp/methods/test_normalize.py
+++ b/pandas/tests/scalar/timestamp/methods/test_normalize.py
@@ -19,3 +19,11 @@ 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_overflow_raises(self):
+        # GH#60583
+        ts = Timestamp.min
+
+        msg = "Cannot normalize Timestamp without integer overflow"
+        with pytest.raises(ValueError, match=msg):
+            ts.normalize()