diff --git a/wp-includes/class-wp-embed.php b/wp-includes/class-wp-embed.php
index 5f22e92a5c..888dcd33da 100644
--- a/wp-includes/class-wp-embed.php
+++ b/wp-includes/class-wp-embed.php
@@ -334,8 +334,12 @@ class WP_Embed {
 		// Replace line breaks from all HTML elements with placeholders.
 		$content = wp_replace_in_html_tags( $content, array( "\n" => '<!-- wp-line-break -->' ) );
 
-		// Find URLs that are on their own line.
-		$content = preg_replace_callback( '|^(\s*)(https?://[^\s"]+)(\s*)$|im', array( $this, 'autoembed_callback' ), $content );
+		if ( preg_match( '#(^|\s|>)https?://#i', $content ) ) {
+			// Find URLs on their own line.
+			$content = preg_replace_callback( '|^(\s*)(https?://[^\s<>"]+)(\s*)$|im', array( $this, 'autoembed_callback' ), $content );
+			// Find URLs in their own paragraph.
+			$content = preg_replace_callback( '|(<p(?: [^>]*)?>\s*)(https?://[^\s<>"]+)(\s*<\/p>)|i', array( $this, 'autoembed_callback' ), $content );
+		}
 
 		// Put the line breaks back.
 		return str_replace( '<!-- wp-line-break -->', "\n", $content );
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 391d4949e2..388123bdd9 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -4,7 +4,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '4.6-alpha-37626';
+$wp_version = '4.6-alpha-37627';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.