diff --git a/src/wp-admin/options-connectors.php b/src/wp-admin/options-connectors.php
index eacb9bdb5f7aa..60e29d158d38a 100644
--- a/src/wp-admin/options-connectors.php
+++ b/src/wp-admin/options-connectors.php
@@ -74,9 +74,15 @@ function _wp_connectors_preload_paths( array $preload_paths ): array {
 }
 add_filter( 'wp_options_connectors_wp_admin_preload_paths', '_wp_connectors_preload_paths' );
 
+// Used to install connector plugins when filesystem credentials are required.
+wp_enqueue_script( 'updates' );
+
 require_once ABSPATH . 'wp-admin/admin-header.php';
 
 // Render the Connectors page.
 wp_options_connectors_wp_admin_render_page();
 
+wp_print_request_filesystem_credentials_modal();
+wp_print_admin_notice_templates();
+
 require_once ABSPATH . 'wp-admin/admin-footer.php';
diff --git a/src/wp-includes/connectors.php b/src/wp-includes/connectors.php
index 88f6a5b964f99..1bf43009bb3a7 100644
--- a/src/wp-includes/connectors.php
+++ b/src/wp-includes/connectors.php
@@ -900,6 +900,7 @@ function _wp_connectors_pass_default_keys_to_ai_client(): void {
  * Exposes connector settings to the connectors-wp-admin script module.
  *
  * @since 7.0.0
+ * @since 7.2.0 Added the `filesystemCredentialsRequired` flag.
  * @access private
  *
  * @param array<string, mixed> $data Existing script module data.
@@ -912,6 +913,10 @@ function _wp_connectors_get_connector_script_module_data( array $data ): array {
 		require_once ABSPATH . 'wp-admin/includes/plugin.php';
 	}
 
+	if ( ! function_exists( 'request_filesystem_credentials' ) ) {
+		require_once ABSPATH . 'wp-admin/includes/file.php';
+	}
+
 	$connectors = array();
 	foreach ( wp_get_connectors() as $connector_id => $connector_data ) {
 		$auth     = $connector_data['authentication'];
@@ -966,6 +971,22 @@ function _wp_connectors_get_connector_script_module_data( array $data ): array {
 	ksort( $connectors );
 	$data['connectors']        = $connectors;
 	$data['isFileModDisabled'] = ! wp_is_file_mod_allowed( 'install_plugins' );
+
+	/*
+	 * The REST API plugins endpoint cannot install plugins when the filesystem
+	 * method requires credentials that have not been stored. In that case, the
+	 * client installs through `wp.updates.installPlugin()` instead, which prompts
+	 * for the credentials with the "Connection Information" modal.
+	 */
+	$data['filesystemCredentialsRequired'] = false;
+	if ( 'direct' !== get_filesystem_method() ) {
+		ob_start();
+		$filesystem_credentials_are_stored = request_filesystem_credentials( self_admin_url() );
+		ob_end_clean();
+
+		$data['filesystemCredentialsRequired'] = ! $filesystem_credentials_are_stored;
+	}
+
 	return $data;
 }
 add_filter( 'script_module_data_options-connectors-wp-admin', '_wp_connectors_get_connector_script_module_data' );
diff --git a/tests/phpunit/tests/connectors/wpConnectorsGetConnectorScriptModuleData.php b/tests/phpunit/tests/connectors/wpConnectorsGetConnectorScriptModuleData.php
index b9b5014affdd1..7512bcf502227 100644
--- a/tests/phpunit/tests/connectors/wpConnectorsGetConnectorScriptModuleData.php
+++ b/tests/phpunit/tests/connectors/wpConnectorsGetConnectorScriptModuleData.php
@@ -209,4 +209,53 @@ public function test_environment_variable_password_may_contain_colons(): void {
 		$this->assertSame( 'env', $auth['keySource'] );
 		$this->assertTrue( $auth['isConnected'] );
 	}
+
+	/**
+	 * @ticket 65223
+	 */
+	public function test_filesystem_credentials_not_required_for_direct_filesystem_method(): void {
+		add_filter(
+			'filesystem_method',
+			static function () {
+				return 'direct';
+			}
+		);
+
+		$data = _wp_connectors_get_connector_script_module_data( array() );
+
+		$this->assertFalse( $data['filesystemCredentialsRequired'] );
+	}
+
+	/**
+	 * @ticket 65223
+	 */
+	public function test_filesystem_credentials_required_when_credentials_are_not_stored(): void {
+		add_filter(
+			'filesystem_method',
+			static function () {
+				return 'ftpext';
+			}
+		);
+
+		$data = _wp_connectors_get_connector_script_module_data( array() );
+
+		$this->assertTrue( $data['filesystemCredentialsRequired'] );
+	}
+
+	/**
+	 * @ticket 65223
+	 */
+	public function test_filesystem_credentials_not_required_when_credentials_are_stored(): void {
+		add_filter(
+			'filesystem_method',
+			static function () {
+				return 'ftpext';
+			}
+		);
+		add_filter( 'request_filesystem_credentials', '__return_true' );
+
+		$data = _wp_connectors_get_connector_script_module_data( array() );
+
+		$this->assertFalse( $data['filesystemCredentialsRequired'] );
+	}
 }