Index: wp-includes/media.php
===================================================================
--- wp-includes/media.php	(revision 24036)
+++ wp-includes/media.php	(working copy)
@@ -1040,6 +1040,7 @@
 		$html .= wp_mediaelement_fallback( $fileurl, $width, $height );
 	$html .= '</video>';
 
+	$html = sprintf( '<div style="width: %dpx; max-width: 100%%;">%s</div>', $width, $html );
 	return apply_filters( 'wp_video_shortcode', $html, $atts, $video, $post_id );
 }
 add_shortcode( 'video', apply_filters( 'wp_video_shortcode_handler', 'wp_video_shortcode' ) );