diff --git a/Misc/NEWS b/Misc/NEWS
index 6a4c05ecc65..63601d8f115 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -71,6 +71,8 @@ Core and Builtins
 Library
 -------
 
+- Properly initialize all fields of a SSL object after allocation.
+
 - Issue #4366: Fix building extensions on all platforms when --enable-shared
   is used.
 
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index 1ae543f155a..448114bd732 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -455,6 +455,7 @@ newPySSLSocket(SSL_CTX *ctx, PySocketSockObject *sock,
     self->peer_cert = NULL;
     self->ssl = NULL;
     self->Socket = NULL;
+    self->shutdown_seen_zero = 0;
 
     /* Make sure the SSL error state is initialized */
     (void) ERR_get_state();