diff --git a/Lib/email/_header_value_parser.py b/Lib/email/_header_value_parser.py
index cb013225ec6..9c55ef7fb45 100644
--- a/Lib/email/_header_value_parser.py
+++ b/Lib/email/_header_value_parser.py
@@ -2047,7 +2047,7 @@ def get_msg_id(value):
        no-fold-literal = "[" *dtext "]"
     """
     msg_id = MsgID()
-    if value[0] in CFWS_LEADER:
+    if value and value[0] in CFWS_LEADER:
         token, value = get_cfws(value)
         msg_id.append(token)
     if not value or value[0] != '<':
diff --git a/Lib/test/test_email/test__header_value_parser.py b/Lib/test/test_email/test__header_value_parser.py
index 7c9f9877d7b..4b5b44258b2 100644
--- a/Lib/test/test_email/test__header_value_parser.py
+++ b/Lib/test/test_email/test__header_value_parser.py
@@ -2583,6 +2583,11 @@ class TestParser(TestParserMixin, TestEmailBase):
 
     # get_msg_id
 
+    def test_get_msg_id_empty(self):
+        # bpo-38708: Test that HeaderParseError is raised and not IndexError.
+        with self.assertRaises(errors.HeaderParseError):
+            parser.get_msg_id('')
+
     def test_get_msg_id_valid(self):
         msg_id = self._test_get_x(
             parser.get_msg_id,
@@ -2694,6 +2699,7 @@ class TestParser(TestParserMixin, TestEmailBase):
         self.assertEqual(msg_id.token_type, 'msg-id')
 
 
+
 @parameterize
 class Test_parse_mime_parameters(TestParserMixin, TestEmailBase):
 
diff --git a/Misc/NEWS.d/next/Library/2019-12-07-22-25-39.bpo-38708.rZTUfk.rst b/Misc/NEWS.d/next/Library/2019-12-07-22-25-39.bpo-38708.rZTUfk.rst
new file mode 100644
index 00000000000..23a0a46d1fe
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-12-07-22-25-39.bpo-38708.rZTUfk.rst
@@ -0,0 +1 @@
+Fix a potential IndexError in email parser when parsing an empty msg-id.