reverted:
--- b/core/modules/media/css/oembed-frame.css
+++ /dev/null
@@ -1,10 +0,0 @@
-iframe {
-  position: absolute;
-  left: 0;
-  top: 0;
-  right: 0;
-  bottom: 0;
-  margin: 0;
-  width: 100%;
-  height: 100%;
-}
diff -u b/core/modules/media/media.libraries.yml b/core/modules/media/media.libraries.yml
--- b/core/modules/media/media.libraries.yml
+++ b/core/modules/media/media.libraries.yml
@@ -15,5 +15,11 @@
-oembed_frame:
+oembed.formatter:
+  version VERSION
+  css:
+    component:
+      css/oembed.formatter.css: {}
+
+oembed.frame:
   version: VERSION
   css:
     component:
-      css/oembed-frame.css: {}
+      css/oembed.frame.css: {}
diff -u b/core/modules/media/src/Controller/OEmbedIframeController.php b/core/modules/media/src/Controller/OEmbedIframeController.php
--- b/core/modules/media/src/Controller/OEmbedIframeController.php
+++ b/core/modules/media/src/Controller/OEmbedIframeController.php
@@ -164,7 +164,7 @@
         '#placeholder_token' => $placeholder_token,
       ];
       if ($scale) {
-        $element['#attached']['library'][] = 'media/oembed_frame';
+        $element['#attached']['library'][] = 'media/oembed.frame';
       }
       $content = $this->renderer->executeInRenderContext(new RenderContext(), function () use ($resource, $element) {
         return $this->renderer->render($element);
diff -u b/core/modules/media/src/Plugin/Field/FieldFormatter/OEmbedFormatter.php b/core/modules/media/src/Plugin/Field/FieldFormatter/OEmbedFormatter.php
--- b/core/modules/media/src/Plugin/Field/FieldFormatter/OEmbedFormatter.php
+++ b/core/modules/media/src/Plugin/Field/FieldFormatter/OEmbedFormatter.php
@@ -223,8 +223,12 @@
             'allowtransparency' => TRUE,
             'width' => $max_width ?: $resource->getWidth(),
             'height' => $max_height ?: $resource->getHeight(),
+            'class' => ['media-oembed-content'],
           ],
         ];
+        if ($scale) {
+          $element[$delta]['#attached']['library'][] = 'media/oembed.formatter';
+        }
 
         CacheableMetadata::createFromObject($resource)
           ->addCacheTags($this->config->getCacheTags())
reverted:
--- b/core/themes/stable/css/media/oembed-frame.css
+++ /dev/null
@@ -1,10 +0,0 @@
-iframe {
-  position: absolute;
-  left: 0;
-  top: 0;
-  right: 0;
-  bottom: 0;
-  margin: 0;
-  width: 100%;
-  height: 100%;
-}
diff -u b/core/themes/stable/stable.info.yml b/core/themes/stable/stable.info.yml
--- b/core/themes/stable/stable.info.yml
+++ b/core/themes/stable/stable.info.yml
@@ -139,10 +139,14 @@
       component:
         css/locale.admin.css: css/locale/locale.admin.css
 
-  media/oembed_frame:
+  media/oembed.formatter:
     css:
       component:
-        css/oembed-frame.css: css/media/oembed-frame.css
+        css/oembed.formatter.css: css/media/oembed.formatter.css
+  media/oembed.frame:
+    css:
+      component:
+        css/oembed.frame.css: css/media/oembed.frame.css
 
   menu_ui/drupal.menu_ui.adminforms:
     css:
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/media/css/oembed.formatter.css
@@ -0,0 +1,3 @@
+.media-oembed-content {
+  max-width: 100%;
+}
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/media/css/oembed.frame.css
@@ -0,0 +1,10 @@
+iframe {
+  position: absolute;
+  left: 0;
+  top: 0;
+  right: 0;
+  bottom: 0;
+  margin: 0;
+  width: 100%;
+  height: 100%;
+}
only in patch2:
unchanged:
--- /dev/null
+++ b/core/themes/stable/css/media/oembed.formatter.css
@@ -0,0 +1,3 @@
+.media-oembed-content {
+  max-width: 100%;
+}
only in patch2:
unchanged:
--- /dev/null
+++ b/core/themes/stable/css/media/oembed.frame.css
@@ -0,0 +1,10 @@
+iframe {
+  position: absolute;
+  left: 0;
+  top: 0;
+  right: 0;
+  bottom: 0;
+  margin: 0;
+  width: 100%;
+  height: 100%;
+}