diff --git a/wp-includes/block-template-utils.php b/wp-includes/block-template-utils.php
index 00b7a4f756..2f2b596c2a 100644
--- a/wp-includes/block-template-utils.php
+++ b/wp-includes/block-template-utils.php
@@ -552,8 +552,8 @@ function _build_block_template_result_from_post( $post ) {
 	}
 
 	$theme          = $terms[0]->name;
-	$has_theme_file = wp_get_theme()->get_stylesheet() === $theme &&
-		null !== _get_block_template_file( $post->post_type, $post->post_name );
+	$template_file = _get_block_template_file( $post->post_type, $post->post_name );
+	$has_theme_file = wp_get_theme()->get_stylesheet() === $theme && null !== $template_file;
 
 	$origin = get_post_meta( $post->ID, 'origin', true );
 
@@ -573,6 +573,10 @@ function _build_block_template_result_from_post( $post ) {
 	$template->is_custom      = true;
 	$template->author         = $post->post_author;
 
+	if ( 'wp_template' === $post->post_type && $has_theme_file && isset( $template_file['postTypes'] ) ) {
+		$template->post_types = $template_file['postTypes'];
+	}
+
 	if ( 'wp_template' === $post->post_type && isset( $default_template_types[ $template->slug ] ) ) {
 		$template->is_custom = false;
 	}
@@ -675,6 +679,13 @@ function get_block_templates( $query = array(), $template_type = 'wp_template' )
 			continue;
 		}
 
+		if ( $post_type &&
+			isset( $template->post_types ) &&
+			! in_array( $post_type, $template->post_types, true )
+		) {
+			continue;
+		}
+
 		$query_result[] = $template;
 	}
 
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 4ac654459d..b37eccdb40 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -16,7 +16,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '6.1-alpha-54183';
+$wp_version = '6.1-alpha-54184';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.