diff -u b/core/modules/system/system.admin.inc b/core/modules/system/system.admin.inc
--- b/core/modules/system/system.admin.inc
+++ b/core/modules/system/system.admin.inc
@@ -211,7 +211,6 @@
   foreach (Element::children($form['modules']) as $key) {
     $module = $form['modules'][$key];
     $module['module_name'] = $module['#module_name'];
-    $module['machine_name'] = $key;
     $module['checkbox'] = $form['uninstall'][$key];
     $module['checkbox_id'] = $form['uninstall'][$key]['#id'];
 
@@ -226,6 +225,7 @@
   foreach (Element::children($form['modules']) as $key) {
     $module = $form['modules'][$key];
     $module['module_name'] = $module['#module_name'];
+    $module['machine_name'] = $key;
     $module['checkbox'] = $form['uninstall'][$key];
     $module['checkbox_id'] = $form['uninstall'][$key]['#id'];
 
only in patch2:
unchanged:
--- a/core/modules/system/tests/src/Functional/Module/UninstallTest.php
+++ b/core/modules/system/tests/src/Functional/Module/UninstallTest.php
@@ -62,6 +62,9 @@ public function testUninstallPage() {
     $this->drupalGet('admin/modules/uninstall');
     $this->assertSession()->titleEquals('Uninstall | Drupal');
 
+    // Make sure the module machine name is rendered in a filter text source.
+    $this->assertSession()->elementTextContains('css', 'tr[data-drupal-selector="edit-module-test"] .module-machine-name.table-filter-text-source', 'module_test');
+
     foreach (\Drupal::service('extension.list.module')->getAllInstalledInfo() as $module => $info) {
       $field_name = "uninstall[$module]";
       if (!empty($info['required'])) {
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/system/tests/src/FunctionalJavascript/System/UninstallFilterTest.php
@@ -0,0 +1,65 @@
+<?php
+
+namespace Drupal\Tests\system\FunctionalJavascript\System;
+
+use Drupal\FunctionalJavascriptTests\WebDriverTestBase;
+
+/**
+ * Tests the modules uninstall filter.
+ *
+ * @group Module
+ */
+class UninstallFilterTest extends WebDriverTestBase {
+
+  /**
+   * Modules to enable.
+   *
+   * @var array
+   */
+  protected static $modules = ['module_test'];
+
+  /**
+   * {@inheritdoc}
+   */
+  protected $defaultTheme = 'stark';
+
+  /**
+   * Tests the modules uninstall filter.
+   */
+  public function testFilter() {
+    $account = $this->drupalCreateUser(['administer modules']);
+    $this->drupalLogin($account);
+
+    $session = $this->getSession();
+
+    $this->drupalGet('admin/modules/uninstall');
+    $filter = $session->getPage()->find('css', '#edit-text');
+
+    // Test filter using module machine name.
+    $filter->setValue('module_test');
+    $session->wait(1000);
+    $result = $this->xpath('//table/tbody/tr[not(contains(@style, :style)) and @data-drupal-selector=:data-drupal-selector]', [
+      ':style' => 'display: none',
+      ':data-drupal-selector' => 'edit-module-test',
+    ]);
+    $this->assertCount(1, $result, 'Module test exists');
+
+    // Test filter using module name.
+    $filter->setValue('Module test');
+    $session->wait(1000);
+    $result = $this->xpath('//table/tbody/tr[not(contains(@style, :style)) and @data-drupal-selector=:data-drupal-selector]', [
+      ':style' => 'display: none',
+      ':data-drupal-selector' => 'edit-module-test',
+    ]);
+    $this->assertCount(1, $result, 'Module test exists');
+
+    // Test non-existing module.
+    $filter->setValue('Cron Queue test');
+    $session->wait(1000);
+    $result = $this->xpath('//table/tbody/tr[not(contains(@style, :style))]', [
+      ':style' => 'display: none',
+    ]);
+    $this->assertCount(0, $result, 'Cron Queue test does not exist');
+  }
+
+}