diff --git a/src/wp-admin/includes/class-wp-site-health.php b/src/wp-admin/includes/class-wp-site-health.php
index 2ddfaadc4b39d..8c6cf8d5cd57d 100644
--- a/src/wp-admin/includes/class-wp-site-health.php
+++ b/src/wp-admin/includes/class-wp-site-health.php
@@ -2187,6 +2187,7 @@ public function get_test_http_requests() {
 	 * This is required for the new block editor to work, so we explicitly test for this.
 	 *
 	 * @since 5.2.0
+	 * @since 7.1.0 Only WordPress' own cookies are sent with the request.
 	 *
 	 * @return array The test results.
 	 */
@@ -2206,7 +2207,16 @@ public function get_test_rest_availability() {
 			'test'        => 'rest_availability',
 		);
 
-		$cookies = wp_unslash( $_COOKIE );
+		/*
+		 * Only WordPress' own cookies have any bearing on this request. Forwarding the rest of
+		 * the browser's cookie jar lets unrelated cookies fail a test that is meant to measure
+		 * the REST API.
+		 */
+		$cookies = array_intersect_key(
+			wp_unslash( $_COOKIE ),
+			array_flip( array( AUTH_COOKIE, SECURE_AUTH_COOKIE, LOGGED_IN_COOKIE, TEST_COOKIE ) )
+		);
+
 		$timeout = 10; // 10 seconds.
 		$headers = array(
 			'Cache-Control' => 'no-cache',
diff --git a/tests/phpunit/tests/admin/wpSiteHealth.php b/tests/phpunit/tests/admin/wpSiteHealth.php
index 6080b477f54c3..43bb453861376 100644
--- a/tests/phpunit/tests/admin/wpSiteHealth.php
+++ b/tests/phpunit/tests/admin/wpSiteHealth.php
@@ -707,4 +707,51 @@ public function test_get_test_opcode_cache_result_by_environment() {
 			$this->assertStringContainsString( __( 'Enabling this cache can significantly improve the performance of your site.' ), $result['description'] );
 		}
 	}
+
+	/**
+	 * Tests that only WordPress' own cookies are sent with the REST API test request.
+	 *
+	 * @ticket 65839
+	 *
+	 * @covers ::get_test_rest_availability()
+	 */
+	public function test_get_test_rest_availability_sends_only_wordpress_cookies() {
+		$original_cookie = $_COOKIE;
+
+		$_COOKIE = array(
+			LOGGED_IN_COOKIE     => 'admin|1700000000|token|hmac',
+			TEST_COOKIE          => 'WP Cookie check',
+			'_ga'                => 'GA1.1.123456789.1700000000',
+			'wp-settings-time-1' => '1700000000',
+		);
+
+		$sent = null;
+
+		add_filter(
+			'pre_http_request',
+			static function ( $response, $parsed_args ) use ( &$sent ) {
+				$sent = $parsed_args['cookies'];
+
+				return array(
+					'response' => array( 'code' => 200 ),
+					'body'     => '',
+				);
+			},
+			10,
+			2
+		);
+
+		$this->instance->get_test_rest_availability();
+
+		$_COOKIE = $original_cookie;
+
+		$this->assertSame(
+			array(
+				LOGGED_IN_COOKIE => 'admin|1700000000|token|hmac',
+				TEST_COOKIE      => 'WP Cookie check',
+			),
+			$sent,
+			'Only WordPress\' own cookies should be sent with the REST API test request.'
+		);
+	}
 }