Index: wp-includes/sitemaps/providers/class-wp-sitemaps-posts.php
===================================================================
--- wp-includes/sitemaps/providers/class-wp-sitemaps-posts.php	(revision 48173)
+++ wp-includes/sitemaps/providers/class-wp-sitemaps-posts.php	(working copy)
@@ -37,6 +37,8 @@
 		$post_types = get_post_types( array( 'public' => true ), 'objects' );
 		unset( $post_types['attachment'] );
 
+		$post_types = array_filter( $post_types, 'is_post_type_viewable' );
+
 		/**
 		 * Filters the list of post object sub types available within the sitemap.
 		 *
Index: wp-includes/sitemaps/providers/class-wp-sitemaps-taxonomies.php
===================================================================
--- wp-includes/sitemaps/providers/class-wp-sitemaps-taxonomies.php	(revision 48173)
+++ wp-includes/sitemaps/providers/class-wp-sitemaps-taxonomies.php	(working copy)
@@ -35,6 +35,8 @@
 	public function get_object_subtypes() {
 		$taxonomies = get_taxonomies( array( 'public' => true ), 'objects' );
 
+		$taxonomies = array_filter( $taxonomies, 'is_taxonomy_viewable' );
+
 		/**
 		 * Filter the list of taxonomy object subtypes available within the sitemap.
 		 *