diff --git a/django/core/mail/message.py b/django/core/mail/message.py
index f3fe6186c7..4f8c93e9e5 100644
--- a/django/core/mail/message.py
+++ b/django/core/mail/message.py
@@ -97,6 +97,8 @@ def sanitize_address(addr, encoding):
             domain = token.domain or ""
     else:
         nm, address = addr
+        if "@" not in address:
+            raise ValueError(f'Invalid address "{address}"')
         localpart, domain = address.rsplit("@", 1)
 
     address_parts = nm + localpart + domain
diff --git a/tests/mail/tests.py b/tests/mail/tests.py
index 54a136c1a9..848ee32e9f 100644
--- a/tests/mail/tests.py
+++ b/tests/mail/tests.py
@@ -1084,9 +1084,10 @@ class MailTests(HeadersCheckMixin, SimpleTestCase):
             "@",
             "to@",
             "@example.com",
+            ("", ""),
         ):
             with self.subTest(email_address=email_address):
-                with self.assertRaises(ValueError):
+                with self.assertRaisesMessage(ValueError, "Invalid address"):
                     sanitize_address(email_address, encoding="utf-8")
 
     def test_sanitize_address_header_injection(self):