diff -u b/core/modules/menu_link_content/menu_link_content.install b/core/modules/menu_link_content/menu_link_content.install
--- b/core/modules/menu_link_content/menu_link_content.install
+++ b/core/modules/menu_link_content/menu_link_content.install
@@ -23,20 +23,25 @@
 function menu_link_content_requirements($phase) {
   $requirements = [];
 
-  // Check for menu_link_content data integrity issues.
-  if (in_array($phase, ['update', 'runtime'], TRUE)) {
-    // The 'enabled' field is non-NULL - if we get a NULL value that indicates a
-    // failure to join on menu_link_content_data.
+  // Check for invalid data before making links revisionable.
+  /** @var \Drupal\Core\Update\UpdateRegistry $registry */
+  $registry = \Drupal::service('update.post_update_registry');
+  $pending_updates = $registry->getPendingUpdateFunctions();
+  $update_name = 'menu_link_content_post_update_make_menu_link_content_revisionable';
+  if ($phase === 'update' && in_array($update_name, $pending_updates, TRUE)) {
+    // The 'enabled' field is non-NULL - if we get a NULL value that indicates
+    // a failure to join on menu_link_content_data.
     $is_broken = \Drupal::entityQuery('menu_link_content')
       ->condition('enabled', NULL, 'IS NULL')
       ->range(0, 1)
       ->accessCheck(FALSE)
       ->execute();
     if ($is_broken) {
-      $requirements['menu_link_content_missing_data'] = [
+      $requirements[$update_name] = [
         'title' => t('Menu link content data'),
         'value' => t("Integrity issues detected"),
-        'description' => t('The menu link content entity type has data integrity issues: you should fix this immediately. See the <a href=":change_record">change record</a> for more information.', [
+        'description' => t('The %update_name function cannot be run until the data has been fixed. See the <a href=":change_record">change record</a> for more information.', [
+          '%update_name' => $update_name . '()',
           ':change_record' => 'https://www.drupal.org/node/3117753',
         ]),
         'severity' => REQUIREMENT_ERROR,
diff -u b/core/modules/menu_link_content/tests/src/Functional/Update/MenuLinkContentUpdateTest.php b/core/modules/menu_link_content/tests/src/Functional/Update/MenuLinkContentUpdateTest.php
--- b/core/modules/menu_link_content/tests/src/Functional/Update/MenuLinkContentUpdateTest.php
+++ b/core/modules/menu_link_content/tests/src/Functional/Update/MenuLinkContentUpdateTest.php
@@ -104,10 +104,7 @@
   }
 
   /**
-   * Test the update hook requirements data integrity check.
-   *
-   * It was added to prevent errors updating menu link content entities to be
-   * revisionable.
+   * Test the update hook requirements check for revisionable menu links.
    *
    * @see menu_link_content_post_update_make_menu_link_content_revisionable()
    * @see menu_link_content_requirements()
@@ -132,7 +129,7 @@
     $this->drupalGet($this->updateUrl);
 
     $this->assertSession()->pageTextContains('Errors found');
-    $this->assertSession()->elementTextContains('css', '.system-status-report__entry--error', 'The menu link content entity type has data integrity issues: you should fix this immediately.');
+    $this->assertSession()->elementTextContains('css', '.system-status-report__entry--error', 'menu_link_content_post_update_make_menu_link_content_revisionable() function cannot be run until the data has been fixed');
   }
 
   /**