diff --git a/src/wp-admin/includes/nav-menu.php b/src/wp-admin/includes/nav-menu.php
index 61657c05ce..30f38e9f56 100644
--- a/src/wp-admin/includes/nav-menu.php
+++ b/src/wp-admin/includes/nav-menu.php
@@ -70,14 +70,19 @@ function _wp_ajax_menu_quick_search( $request = array() ) {
 
 	} elseif ( preg_match('/quick-search-(posttype|taxonomy)-([a-zA-Z_-]*\b)/', $type, $matches) ) {
 		if ( 'posttype' == $matches[1] && get_post_type_object( $matches[2] ) ) {
-			$search_results_query = new WP_Query( array(
+			$post_type_obj = _wp_nav_menu_meta_box_object( get_post_type_object( $matches[2] ) );
+			$args = array(
 				'no_found_rows'          => true,
 				'update_post_meta_cache' => false,
 				'update_post_term_cache' => false,
 				'posts_per_page'         => 10,
 				'post_type'              => $matches[2],
 				's'                      => $query,
-			) );
+			);
+			if ( isset( $post_type_obj->_default_query ) ) {
+				$args = array_merge( $args, (array) $post_type_obj->_default_query );
+			}
+			$search_results_query = new WP_Query( $args );
 			if ( ! $search_results_query->have_posts() ) {
 				return;
 			}
diff --git a/tests/phpunit/tests/menu/wpAjaxMenuQuickSearch.php b/tests/phpunit/tests/menu/wpAjaxMenuQuickSearch.php
index 54fa9cfdb6..c622b566ee 100644
--- a/tests/phpunit/tests/menu/wpAjaxMenuQuickSearch.php
+++ b/tests/phpunit/tests/menu/wpAjaxMenuQuickSearch.php
@@ -6,6 +6,33 @@
 class Tests_Menu_WpAjaxMenuQuickSeach extends WP_UnitTestCase {
 
 	/**
+	 * Current screen.
+	 *
+	 * @var mixed
+	 */
+	protected $current_screen;
+
+	/**
+	 * Set up. Workaround set_current_screen( null ) not working due to $hook_suffix not being set.
+	 */
+	function setUp() {
+		global $current_screen;
+		$this->current_screen = $current_screen;
+		parent::setUp();
+	}
+
+	/**
+	 * Tear down. Workaround set_current_screen( null ) not working due to $hook_suffix not being set.
+	 */
+	function tearDown() {
+		global $current_screen;
+		parent::tearDown();
+		$current_screen = $this->current_screen;
+	}
+
+	/**
+	 * Test search returns results for pages.
+	 *
 	 * @ticket 27042
 	 */
 	public function test_search_returns_results_for_pages() {
@@ -26,4 +53,31 @@ class Tests_Menu_WpAjaxMenuQuickSeach extends WP_UnitTestCase {
 		$results = explode( "\n", trim( $output ) );
 		$this->assertCount( 3, $results );
 	}
+
+	/**
+	 * Test that search only returns results for publihed posts.
+	 *
+	 * @ticket 33742
+	 */
+	public function test_search_returns_results_for_published_posts() {
+		require_once ABSPATH . 'wp-admin/includes/nav-menu.php';
+
+		// This will make sure that WP_Query sets is_admin to true.
+		set_current_screen( 'nav-menu.php' );
+
+		self::factory()->post->create( array( 'post_type' => 'post', 'post_status' => 'publish', 'post_title' => 'Publish', 'post_content' => 'FOO' ) );
+		self::factory()->post->create( array( 'post_type' => 'post', 'post_status' => 'draft', 'post_title' => 'Draft', 'post_content' => 'FOO' ) );
+		self::factory()->post->create( array( 'post_type' => 'post', 'post_status' => 'pending', 'post_title' => 'Pending', 'post_content' => 'FOO' ) );
+		self::factory()->post->create( array( 'post_type' => 'post', 'post_status' => 'future', 'post_title' => 'Future', 'post_content' => 'FOO', 'post_date' => gmdate( 'Y-m-d H:i:s', strtotime( '+1 month' ) ) ) );
+
+		$request = array(
+			'type' => 'quick-search-posttype-post',
+			'q' => 'FOO',
+		);
+		$output = get_echo( '_wp_ajax_menu_quick_search', array( $request ) );
+
+		$this->assertNotEmpty( $output );
+		$results = explode( "\n", trim( $output ) );
+		$this->assertCount( 1, $results );
+	}
 }