diff -u b/core/modules/page_cache/src/StackMiddleware/PageCache.php b/core/modules/page_cache/src/StackMiddleware/PageCache.php
--- b/core/modules/page_cache/src/StackMiddleware/PageCache.php
+++ b/core/modules/page_cache/src/StackMiddleware/PageCache.php
@@ -7,7 +7,7 @@
 use Drupal\Core\Cache\CacheBackendInterface;
 use Drupal\Core\PageCache\RequestPolicyInterface;
 use Drupal\Core\PageCache\ResponsePolicyInterface;
-use Drupal\Core\Site\Settings
+use Drupal\Core\Site\Settings;
 use Symfony\Component\HttpFoundation\BinaryFileResponse;
 use Symfony\Component\HttpFoundation\Request;
 use Symfony\Component\HttpFoundation\Response;
@@ -249,10 +249,30 @@
     // - Get the time expiration from the Expires header, rather than the
     //   interface, but see https://www.drupal.org/node/2352009 about possibly
     //   changing that.
-    $tags = $response->getCacheableMetadata()->getCacheTags();
-    $date = $response->getExpires()->getTimestamp();
-    $expire = ($date > time()) ? $date : Cache::PERMANENT;
-    $this->set($request, $response, $expire, $tags);
+    $expire = FALSE;
+    // 404 responses can fill non-LRU cache backends and generally are likely to
+    // have a low cache hit rate. So do not cache them permanently.
+    if ($response->getStatusCode() === $response::HTTP_NOT_FOUND) {
+      // Cache for an hour by default, or the max age, whichever is the smaller.
+      // If the ttl is set to FALSE then do not cache it.
+      $settings_ttl = Settings::get('404_cache_ttl', 3600);
+      if ($settings_ttl) {
+        $max_age = $response->getMaxAge();
+        // The response's max_age will be negative in the case the response has
+        // no time set.
+        $ttl = ($max_age > 0) ? min($max_age, $settings_ttl) : $settings_ttl;
+        $expire = REQUEST_TIME + $ttl;
+      }
+    }
+    else {
+      $date = $response->getExpires()->getTimestamp();
+      $expire = ($date > time()) ? $date : Cache::PERMANENT;
+    }
+
+    if ($expire !== FALSE) {
+      $tags = $response->getCacheableMetadata()->getCacheTags();
+      $this->set($request, $response, $expire, $tags);
+    }
 
     // Mark response as a cache miss.
     $response->headers->set('X-Drupal-Cache', 'MISS');
@@ -308,17 +328,6 @@
    */
   protected function set(Request $request, Response $response, $expire, array $tags) {
     $cid = $this->getCacheId($request);
-
-    // 404 responses can fill non-LRU cache backends and generally are likely to
-    // have a low cache hit rate. So do not cache them permanently.
-    if ($response->getStatusCode() == $response::HTTP_NOT_FOUND) {
-      $max_age = $response->getMaxAge();
-
-      // Cache for an hour by default, or the max age, whichever is the greater.
-      $ttl = Settings::get('404_cache_ttl', 3600);
-      $expire = REQUEST_TIME + min($max_age, $ttl);
-    }
-
     $this->cache->set($cid, $response, $expire, $tags);
   }
 
only in patch2:
unchanged:
--- a/core/modules/page_cache/src/Tests/PageCacheTest.php
+++ b/core/modules/page_cache/src/Tests/PageCacheTest.php
@@ -375,6 +375,21 @@ function testPageCacheAnonymous403404() {
       $this->assertResponse($code);
       $this->assertEqual($this->drupalGetHeader('X-Drupal-Cache'), 'MISS');
     }
+
+    // Disable 404 caching
+    $settings['settings']['404_cache_ttl'] = (object) array(
+      'value' => FALSE,
+      'required' => TRUE,
+    );
+    $this->writeSettings($settings);
+    \Drupal::service('cache.render')->deleteAll();
+
+    // Getting the 404 page twice you still result in a cache miss.
+    $this->drupalGet($invalid_url);
+    $this->drupalGet($invalid_url);
+    $this->assertResponse(404);
+    $this->assertEqual($this->drupalGetHeader('X-Drupal-Cache'), 'MISS');
+
   }
 
   /**