diff --git a/core/modules/page_cache/src/StackMiddleware/PageCache.php b/core/modules/page_cache/src/StackMiddleware/PageCache.php
index f25c685..a2792a3 100644
--- a/core/modules/page_cache/src/StackMiddleware/PageCache.php
+++ b/core/modules/page_cache/src/StackMiddleware/PageCache.php
@@ -312,6 +312,14 @@ protected function get(Request $request, $allow_invalid = FALSE) {
    */
   protected function set(Request $request, Response $response, $expire, array $tags) {
     $cid = $this->getCacheId($request);
+
+    // Do not store 404 responses in the cache for longer than an hour.
+    if ($response->getStatusCode() == $response::HTTP_NOT_FOUND) {
+      $max_age = $response->getMaxAge();
+      // Cache for an hour or the maximum age, which ever is the greater.
+      $expire = REQUEST_TIME + min($max_age, 3600);
+    }
+
     $this->cache->set($cid, $response, $expire, $tags);
   }