diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 1c99ba0b8e412..86fa9083a33cf 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -909,6 +909,8 @@ Timezones
 - Bug in :meth:`Series.astype` and :meth:`DataFrame.astype` with object-dtype containing multiple timezone-aware ``datetime`` objects with heterogeneous timezones to a :class:`DatetimeTZDtype` incorrectly raising (:issue:`32581`)
 - Bug in :func:`to_datetime` was failing to parse date strings with timezone name when ``format`` was specified with ``%Z`` (:issue:`49748`)
 - Better error message when passing invalid values to ``ambiguous`` parameter in :meth:`Timestamp.tz_localize` (:issue:`49565`)
+- Bug in string parsing incorrectly allowing a :class:`Timestamp` to be constructed with an invalid timezone, which would raise when trying to print (:issue:`50668`)
+-
 
 Numeric
 ^^^^^^^
diff --git a/pandas/_libs/tslibs/parsing.pyx b/pandas/_libs/tslibs/parsing.pyx
index dabeab3e30f4d..3bc422942276f 100644
--- a/pandas/_libs/tslibs/parsing.pyx
+++ b/pandas/_libs/tslibs/parsing.pyx
@@ -304,6 +304,19 @@ def parse_datetime_string(
         raise OutOfBoundsDatetime(
             f'Parsing "{date_string}" to datetime overflows'
             ) from err
+    if dt.tzinfo is not None:
+        # dateutil can return a datetime with a tzoffset outside of (-24H, 24H)
+        #  bounds, which is invalid (can be constructed, but raises if we call
+        #  str(dt)).  Check that and raise here if necessary.
+        try:
+            dt.utcoffset()
+        except ValueError as err:
+            # offset must be a timedelta strictly between -timedelta(hours=24)
+            #  and timedelta(hours=24)
+            raise ValueError(
+                f'Parsed string "{date_string}" gives an invalid tzoffset, '
+                "which must be between -timedelta(hours=24) and timedelta(hours=24)"
+            )
 
     return dt
 
diff --git a/pandas/tests/scalar/timestamp/test_constructors.py b/pandas/tests/scalar/timestamp/test_constructors.py
index aa5a55e6ca39d..8ee92e28b78bf 100644
--- a/pandas/tests/scalar/timestamp/test_constructors.py
+++ b/pandas/tests/scalar/timestamp/test_constructors.py
@@ -24,6 +24,16 @@
 
 
 class TestTimestampConstructors:
+    def test_construct_from_string_invalid_raises(self):
+        # dateutil (weirdly) parses "200622-12-31" as
+        #  datetime(2022, 6, 20, 12, 0, tzinfo=tzoffset(None, -111600)
+        #  which besides being mis-parsed, is a tzoffset that will cause
+        #  str(ts) to raise ValueError.  Ensure we raise in the constructor
+        #  instead.
+        # see test_to_datetime_malformed_raise for analogous to_datetime test
+        with pytest.raises(ValueError, match="gives an invalid tzoffset"):
+            Timestamp("200622-12-31")
+
     def test_constructor_from_iso8601_str_with_offset_reso(self):
         # GH#49737
         ts = Timestamp("2016-01-01 04:05:06-01:00")
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index dd1012d57d6bc..a6e40c30d5b82 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -1561,12 +1561,14 @@ def test_to_datetime_malformed_no_raise(self, errors, expected):
     def test_to_datetime_malformed_raise(self):
         # GH 48633
         ts_strings = ["200622-12-31", "111111-24-11"]
+        msg = (
+            'Parsed string "200622-12-31" gives an invalid tzoffset, which must '
+            r"be between -timedelta\(hours=24\) and timedelta\(hours=24\), "
+            "at position 0"
+        )
         with pytest.raises(
             ValueError,
-            match=(
-                r"^offset must be a timedelta strictly between "
-                r"-timedelta\(hours=24\) and timedelta\(hours=24\)., at position 0$"
-            ),
+            match=msg,
         ):
             with tm.assert_produces_warning(
                 UserWarning, match="Could not infer format"