diff --git a/ssl/statem/statem_lib.c b/ssl/statem/statem_lib.c
index 44cf5a6ce0..d5def193a0 100644
--- a/ssl/statem/statem_lib.c
+++ b/ssl/statem/statem_lib.c
@@ -1515,8 +1515,8 @@ static int ssl_method_error(const SSL *s, const SSL_METHOD *method)
 
 /*
  * Only called by servers. Returns 1 if the server has a TLSv1.3 capable
- * certificate type, or has PSK or a certificate callback configured. Otherwise
- * returns 0.
+ * certificate type, or has PSK or a certificate callback configured, or has
+ * a servername callback configure. Otherwise returns 0.
  */
 static int is_tls13_capable(const SSL *s)
 {
@@ -1525,6 +1525,17 @@ static int is_tls13_capable(const SSL *s)
     int curve;
 #endif
 
+    if (!ossl_assert(s->ctx != NULL) || !ossl_assert(s->session_ctx != NULL))
+        return 0;
+
+    /*
+     * A servername callback can change the available certs, so if a servername
+     * cb is set then we just assume TLSv1.3 will be ok
+     */
+    if (s->ctx->ext.servername_cb != NULL
+            || s->session_ctx->ext.servername_cb != NULL)
+        return 1;
+
 #ifndef OPENSSL_NO_PSK
     if (s->psk_server_callback != NULL)
         return 1;