diff --git a/Lib/_strptime.py b/Lib/_strptime.py
index 5df37f5f4b8..b97dfcce1e8 100644
--- a/Lib/_strptime.py
+++ b/Lib/_strptime.py
@@ -201,7 +201,7 @@ def __init__(self, locale_time=None):
             #XXX: Does 'Y' need to worry about having less or more than
             #     4 digits?
             'Y': r"(?P<Y>\d\d\d\d)",
-            'z': r"(?P<z>[+-]\d\d:?[0-5]\d(:?[0-5]\d(\.\d{1,6})?)?|Z)",
+            'z': r"(?P<z>[+-]\d\d:?[0-5]\d(:?[0-5]\d(\.\d{1,6})?)?|(?-i:Z))",
             'A': self.__seqToRE(self.locale_time.f_weekday, 'A'),
             'a': self.__seqToRE(self.locale_time.a_weekday, 'a'),
             'B': self.__seqToRE(self.locale_time.f_month[1:], 'B'),
diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
index 775d3151ae2..316cf0b8da7 100644
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -2609,6 +2609,7 @@ def test_strptime(self):
 
         with self.assertRaises(ValueError): strptime("-2400", "%z")
         with self.assertRaises(ValueError): strptime("-000", "%z")
+        with self.assertRaises(ValueError): strptime("z", "%z")
 
     def test_strptime_single_digit(self):
         # bpo-34903: Check that single digit dates and times are allowed.
diff --git a/Misc/NEWS.d/next/Library/2021-02-22-22-54-40.bpo-43295.h_ffu7.rst b/Misc/NEWS.d/next/Library/2021-02-22-22-54-40.bpo-43295.h_ffu7.rst
new file mode 100644
index 00000000000..ac9a5c96c9c
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-02-22-22-54-40.bpo-43295.h_ffu7.rst
@@ -0,0 +1,2 @@
+:meth:`datetime.datetime.strptime` now raises ``ValueError`` instead of
+``IndexError`` when matching ``'z'`` with the ``%z`` format specifier.