diff --git a/src/wp-includes/default-filters.php b/src/wp-includes/default-filters.php
index 783606df4b..7e0ecd64d3 100644
--- a/src/wp-includes/default-filters.php
+++ b/src/wp-includes/default-filters.php
@@ -238,6 +238,7 @@ add_filter( 'wp_mail', 'wp_staticize_emoji_for_email' );
 
 // Robots filters.
 add_filter( 'wp_robots', 'wp_robots_noindex' );
+add_filter( 'wp_robots', 'wp_robots_noindex_embeds' );
 add_filter( 'wp_robots', 'wp_robots_noindex_search' );
 add_filter( 'wp_robots', 'wp_robots_max_image_preview_large' );
 
@@ -611,7 +612,6 @@ add_action( 'embed_footer', 'print_embed_sharing_dialog' );
 add_action( 'embed_footer', 'print_embed_scripts' );
 add_action( 'embed_footer', 'wp_print_footer_scripts', 20 );
 
-add_filter( 'wp_robots', 'wp_embed_no_robots' );
 add_filter( 'excerpt_more', 'wp_embed_excerpt_more', 20 );
 add_filter( 'the_excerpt_embed', 'wptexturize' );
 add_filter( 'the_excerpt_embed', 'convert_chars' );
diff --git a/src/wp-includes/embed.php b/src/wp-includes/embed.php
index 5336b187f2..7c5ac83f24 100644
--- a/src/wp-includes/embed.php
+++ b/src/wp-includes/embed.php
@@ -1243,23 +1243,3 @@ function wp_filter_pre_oembed_result( $result, $url, $args ) {
 
 	return $result;
 }
-
-/**
- * Adds noindex to the robots meta tag for embeds.
- *
- * Typical usage is as a {@see 'wp_robots'} callback:
- *
- *     add_filter( 'wp_robots', 'wp_embed_no_robots' );
- *
- * @since 5.7.0
- *
- * @param array $robots Associative array of robots directives.
- * @return array Filtered robots directives.
- */
-function wp_embed_no_robots( array $robots ) {
-	if ( ! is_embed() ) {
-		return $robots;
-	}
-
-	return wp_robots_no_robots( $robots );
-}
diff --git a/src/wp-includes/robots-template.php b/src/wp-includes/robots-template.php
index 61931a25e5..19c7699790 100644
--- a/src/wp-includes/robots-template.php
+++ b/src/wp-includes/robots-template.php
@@ -74,6 +74,7 @@ function wp_robots() {
  *     add_filter( 'wp_robots', 'wp_robots_noindex' );
  *
  * @since 5.7.0
+ *
  * @see wp_robots_no_robots()
  *
  * @param array $robots Associative array of robots directives.
@@ -87,6 +88,28 @@ function wp_robots_noindex( array $robots ) {
 	return $robots;
 }
 
+/**
+ * Adds noindex to the robots meta tag for embeds.
+ *
+ * Typical usage is as a {@see 'wp_robots'} callback:
+ *
+ *     add_filter( 'wp_robots', 'wp_robots_noindex_embeds' );
+ *
+ * @since 5.7.0
+ *
+ * @see wp_robots_no_robots()
+ *
+ * @param array $robots Associative array of robots directives.
+ * @return array Filtered robots directives.
+ */
+function wp_robots_noindex_embeds( array $robots ) {
+	if ( is_embed() ) {
+		return wp_robots_no_robots( $robots );
+	}
+
+	return $robots;
+}
+
 /**
  * Adds noindex to the robots meta tag if a search is being performed.
  *
@@ -99,6 +122,7 @@ function wp_robots_noindex( array $robots ) {
  *     add_filter( 'wp_robots', 'wp_robots_noindex_search' );
  *
  * @since 5.7.0
+ *
  * @see wp_robots_no_robots()
  *
  * @param array $robots Associative array of robots directives.