diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index cd1cb0b64f74a..31dc4b8dccb8c 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -101,7 +101,6 @@ Other enhancements
 - :meth:`~pandas.core.groupby.GroupBy.transform` has gained ``engine`` and ``engine_kwargs`` arguments that supports executing functions with ``Numba`` (:issue:`32854`)
 - :meth:`~pandas.core.resample.Resampler.interpolate` now supports SciPy interpolation method :class:`scipy.interpolate.CubicSpline` as method ``cubicspline`` (:issue:`33670`)
 -
-
 .. ---------------------------------------------------------------------------
 
 Increased minimum versions for dependencies
@@ -462,6 +461,8 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.to_period` not infering the frequency when called with no arguments (:issue:`33358`)
 - Bug in :meth:`DatetimeIndex.tz_localize` incorrectly retaining ``freq`` in some cases where the original freq is no longer valid (:issue:`30511`)
 - Bug in :meth:`DatetimeIndex.intersection` losing ``freq`` and timezone in some cases (:issue:`33604`)
+- ``OutOfBoundsDatetime`` issues an error message when timestamp is out of implementation bounds. (:issue:`32967`)
+
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 5a8d0a0ec1670..e12ec4e8f9c6c 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -523,10 +523,14 @@ cdef inline check_overflows(_TSObject obj):
     # GH#12677
     if obj.dts.year == 1677:
         if not (obj.value < 0):
-            raise OutOfBoundsDatetime
+            raise OutOfBoundsDatetime(
+                f'Timestamp cannot be converted within implementation bounds'
+            )
     elif obj.dts.year == 2262:
         if not (obj.value > 0):
-            raise OutOfBoundsDatetime
+            raise OutOfBoundsDatetime(
+                f'Timestamp cannot be converted within implementation bounds'
+            )
 
 
 # ----------------------------------------------------------------------
diff --git a/pandas/tests/scalar/timestamp/test_timezones.py b/pandas/tests/scalar/timestamp/test_timezones.py
index 9611c827be6fe..bd49467695d00 100644
--- a/pandas/tests/scalar/timestamp/test_timezones.py
+++ b/pandas/tests/scalar/timestamp/test_timezones.py
@@ -25,6 +25,7 @@ def test_tz_localize_pushes_out_of_bounds(self):
         # GH#12677
         # tz_localize that pushes away from the boundary is OK
         pac = Timestamp.min.tz_localize("US/Pacific")
+        msg = "Timestamp cannot be converted within implementation bounds"
         assert pac.value > Timestamp.min.value
         pac.tz_convert("Asia/Tokyo")  # tz_convert doesn't change value
         with pytest.raises(OutOfBoundsDatetime, match=msg):