diff --git a/Lib/email/_parseaddr.py b/Lib/email/_parseaddr.py
index 4d27f87..977fedf 100644
--- a/Lib/email/_parseaddr.py
+++ b/Lib/email/_parseaddr.py
@@ -67,6 +67,8 @@ def _parsedate_tz(data):
     if not data:
         return None
     data = data.split()
+    if not data:  # This happens for whitespace-only input.
+        return None
     # The FWS after the comma after the day-of-week is optional, so search and
     # adjust for this.
     if data[0].endswith(',') or data[0].lower() in _daynames:
diff --git a/Lib/test/test_email/test_email.py b/Lib/test/test_email/test_email.py
index 0154bba..4001f71 100644
--- a/Lib/test/test_email/test_email.py
+++ b/Lib/test/test_email/test_email.py
@@ -3003,6 +3003,8 @@ def test_formatdate_usegmt(self):
     def test_parsedate_returns_None_for_invalid_strings(self):
         self.assertIsNone(utils.parsedate(''))
         self.assertIsNone(utils.parsedate_tz(''))
+        self.assertIsNone(utils.parsedate(' '))
+        self.assertIsNone(utils.parsedate_tz(' '))
         self.assertIsNone(utils.parsedate('0'))
         self.assertIsNone(utils.parsedate_tz('0'))
         self.assertIsNone(utils.parsedate('A Complete Waste of Time'))
diff --git a/Misc/NEWS.d/next/Library/2021-08-26-16-25-48.bpo-45001.tn_dKp.rst b/Misc/NEWS.d/next/Library/2021-08-26-16-25-48.bpo-45001.tn_dKp.rst
new file mode 100644
index 0000000..55cc409
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-08-26-16-25-48.bpo-45001.tn_dKp.rst
@@ -0,0 +1,2 @@
+Made email date parsing more robust against malformed input, namely a
+whitespace-only ``Date:`` header. Patch by Wouter Bolsterlee.