diff --git a/wp-includes/rest-api/class-wp-rest-server.php b/wp-includes/rest-api/class-wp-rest-server.php
index 9df4556ada..50e7bd9796 100644
--- a/wp-includes/rest-api/class-wp-rest-server.php
+++ b/wp-includes/rest-api/class-wp-rest-server.php
@@ -1273,10 +1273,23 @@ class WP_REST_Server {
 		);
 
 		$response = new WP_REST_Response( $available );
-		$response->add_link( 'help', 'https://developer.wordpress.org/rest-api/' );
-		$this->add_active_theme_link_to_index( $response );
-		$this->add_site_logo_to_index( $response );
-		$this->add_site_icon_to_index( $response );
+
+		$fields = isset( $request['_fields'] ) ? $request['_fields'] : '';
+		$fields = wp_parse_list( $fields );
+		if ( empty( $fields ) ) {
+			$fields[] = '_links';
+		}
+
+		if ( $request->has_param( '_embed' ) ) {
+			$fields[] = '_embedded';
+		}
+
+		if ( rest_is_field_included( '_links', $fields ) || rest_is_field_included( '_embedded', $fields ) ) {
+			$response->add_link( 'help', 'https://developer.wordpress.org/rest-api/' );
+			$this->add_active_theme_link_to_index( $response );
+			$this->add_site_logo_to_index( $response );
+			$this->add_site_icon_to_index( $response );
+		}
 
 		/**
 		 * Filters the REST API root index data.
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 4fba75fd1c..9ba4c26aa1 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -16,7 +16,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '6.4-alpha-56565';
+$wp_version = '6.4-alpha-56566';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.