diff --git a/django/core/mail/backends/smtp.py b/django/core/mail/backends/smtp.py
index 05006a2b17..f8392918b2 100644
--- a/django/core/mail/backends/smtp.py
+++ b/django/core/mail/backends/smtp.py
@@ -1,5 +1,6 @@
 """SMTP email backend class."""
 import smtplib
+import socket
 import ssl
 import threading
 
@@ -71,7 +72,7 @@ class EmailBackend(BaseEmailBackend):
             if self.username and self.password:
                 self.connection.login(force_str(self.username), force_str(self.password))
             return True
-        except smtplib.SMTPException:
+        except (smtplib.SMTPException, socket.error) as e:
             if not self.fail_silently:
                 raise
 
diff --git a/tests/mail/tests.py b/tests/mail/tests.py
index e518ca46d5..1bb7236032 100644
--- a/tests/mail/tests.py
+++ b/tests/mail/tests.py
@@ -7,6 +7,7 @@ import mimetypes
 import os
 import shutil
 import smtpd
+import socket
 import sys
 import tempfile
 import threading
@@ -1448,6 +1449,9 @@ class SMTPBackendTests(BaseEmailBackendTests, SMTPBackendTestsBase):
         finally:
             SMTP.send = send
 
+
+class SMTPNoServerTests(SimpleTestCase):
+
     def test_send_messages_after_open_failed(self):
         """
         send_messages() shouldn't try to send messages if open() raises an
@@ -1461,6 +1465,16 @@ class SMTPBackendTests(BaseEmailBackendTests, SMTPBackendTestsBase):
         email = EmailMessage('Subject', 'Content', 'from@example.com', ['to@example.com'])
         self.assertEqual(backend.send_messages([email]), None)
 
+    def test_fail_silently_on_connection_error(self):
+        """
+        A socket connection error is silenced with fail_silently=True.
+        """
+        backend = smtp.EmailBackend(username='', password='')
+        with self.assertRaises(socket.error):
+            backend.open()
+        backend.fail_silently = True
+        backend.open()
+
 
 class SMTPBackendStoppedServerTest(SMTPBackendTestsBase):
     """