diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 686c5ad0165e7..ea0a002a27f8e 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -28,6 +28,8 @@ Other Enhancements
 Backwards incompatible API changes
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+- :meth:`Timestamp.strptime` will now rise a NotImplementedError (:issue:`21257`)
+
 .. _whatsnew_0250.api.other:
 
 Other API Changes
diff --git a/pandas/_libs/tslibs/nattype.pyx b/pandas/_libs/tslibs/nattype.pyx
index a13fcfdc855d5..79e2e256c501d 100644
--- a/pandas/_libs/tslibs/nattype.pyx
+++ b/pandas/_libs/tslibs/nattype.pyx
@@ -374,7 +374,6 @@ class NaTType(_NaT):
     utctimetuple = _make_error_func('utctimetuple', datetime)
     timetz = _make_error_func('timetz', datetime)
     timetuple = _make_error_func('timetuple', datetime)
-    strptime = _make_error_func('strptime', datetime)
     strftime = _make_error_func('strftime', datetime)
     isocalendar = _make_error_func('isocalendar', datetime)
     dst = _make_error_func('dst', datetime)
@@ -388,6 +387,14 @@ class NaTType(_NaT):
     # The remaining methods have docstrings copy/pasted from the analogous
     # Timestamp methods.
 
+    strptime = _make_error_func('strptime',  # noqa:E128
+        """
+        Timestamp.strptime(string, format)
+
+        Function is not implemented. Use pd.to_datetime().
+        """
+    )
+
     utcfromtimestamp = _make_error_func('utcfromtimestamp',  # noqa:E128
         """
         Timestamp.utcfromtimestamp(ts)
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index a2929dbeb471f..8d825e0a6179e 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -697,6 +697,17 @@ class Timestamp(_Timestamp):
         """
         return cls(datetime.fromtimestamp(ts))
 
+    # Issue 25016.
+    @classmethod
+    def strptime(cls, date_string, format):
+        """
+        Timestamp.strptime(string, format)
+
+        Function is not implemented. Use pd.to_datetime().
+        """
+        raise NotImplementedError("Timestamp.strptime() is not implmented."
+                                  "Use to_datetime() to parse date strings.")
+
     @classmethod
     def combine(cls, date, time):
         """
diff --git a/pandas/tests/scalar/timestamp/test_timestamp.py b/pandas/tests/scalar/timestamp/test_timestamp.py
index f42fad4c925f0..7d81d905eac4f 100644
--- a/pandas/tests/scalar/timestamp/test_timestamp.py
+++ b/pandas/tests/scalar/timestamp/test_timestamp.py
@@ -355,6 +355,14 @@ def test_constructor_invalid_tz(self):
             # interpreted as a `freq`
             Timestamp('2012-01-01', 'US/Pacific')
 
+    def test_constructor_strptime(self):
+        # GH25016
+        # Test support for Timestamp.strptime
+        fmt = '%Y%m%d-%H%M%S-%f%z'
+        ts = '20190129-235348-000001+0000'
+        with pytest.raises(NotImplementedError):
+            Timestamp.strptime(ts, fmt)
+
     def test_constructor_tz_or_tzinfo(self):
         # GH#17943, GH#17690, GH#5168
         stamps = [Timestamp(year=2017, month=10, day=22, tz='UTC'),