diff --git a/src/wp-admin/includes/class-wp-site-health-auto-updates.php b/src/wp-admin/includes/class-wp-site-health-auto-updates.php
index 3483bfae91..e965aa3849 100644
--- a/src/wp-admin/includes/class-wp-site-health-auto-updates.php
+++ b/src/wp-admin/includes/class-wp-site-health-auto-updates.php
@@ -90,7 +90,7 @@ class WP_Site_Health_Auto_Updates {
 	 * @return array The test results.
 	 */
 	public function test_wp_version_check_attached() {
-		if ( ! has_filter( 'wp_version_check', 'wp_version_check' ) ) {
+		if ( ( ! is_multisite() || ( is_main_site() && is_network_admin() ) ) && ! has_filter( 'wp_version_check', 'wp_version_check' ) ) {
 			return array(
 				'description' => sprintf(
 					/* translators: %s: Name of the filter used. */