diff --git a/core/includes/update.inc b/core/includes/update.inc
index 9fc38226245b135614946d1187280fe655cb5a35..4643666bdd2a1b6e7d272281ec902e6bbad4f19f 100644
--- a/core/includes/update.inc
+++ b/core/includes/update.inc
@@ -14,8 +14,15 @@
 
 /**
  * Tests the compatibility of a module or theme.
+ *
+ * @deprecated in drupal:9.1.0 and is removed from drupal:10.0.0. No direct
+ *   replacement is provided.
+ *
+ * @see https://www.drupal.org/node/3150727
+ * @see \Drupal\Core\Extension\ExtensionList::checkIncompatibility()
  */
 function update_check_incompatibility($name, $type = 'module') {
+  @trigger_error('update_check_incompatibility() is deprecated in drupal:9.1.0 and is removed from drupal:10.0.0. No direct replacement is provided. See https://www.drupal.org/node/3150727', E_USER_DEPRECATED);
   static $themes, $modules;
 
   // Store values of expensive functions for future use.
diff --git a/core/tests/Drupal/KernelTests/Core/Extension/UpdateDeprecationTest.php b/core/tests/Drupal/KernelTests/Core/Extension/UpdateDeprecationTest.php
new file mode 100644
index 0000000000000000000000000000000000000000..e51e35e05fe0871ff9d530334dec7a1027bf5a44
--- /dev/null
+++ b/core/tests/Drupal/KernelTests/Core/Extension/UpdateDeprecationTest.php
@@ -0,0 +1,35 @@
+<?php
+
+namespace Drupal\KernelTests\Core\Extension;
+
+use Drupal\KernelTests\KernelTestBase;
+
+/**
+ * Tests deprecated update.inc functions.
+ *
+ * @group legacy
+ * @group extension
+ */
+class UpdateDeprecationTest extends KernelTestBase {
+
+  /**
+   * {@inheritdoc}
+   */
+  protected function setUp(): void {
+    parent::setUp();
+
+    // Include the legacy update.inc file.
+    include_once $this->root . '/core/includes/update.inc';
+  }
+
+  /**
+   * Tests update_check_incompatibility() function.
+   *
+   * @expectedDeprecation update_check_incompatibility() is deprecated in drupal:9.1.0 and is removed from drupal:10.0.0. No direct replacement is provided. See https://www.drupal.org/node/3150727
+   */
+  public function testUpdateCheckIncompatibility() {
+    $this->assertTrue(update_check_incompatibility('incompatible_module'));
+    $this->assertFalse(update_check_incompatibility('system'));
+  }
+
+}