The suspect fled the scene after his car left the road on Rudding Lane, near the Rudding Park Hotel in Follifoot on Monday night.
Officers managed to catch the driver, who gave a positive breath sample when tested at a police station.
He was arrested but released under investigation to receive treatment for a broken arm.
Rudding Park is where Leeds United manager Marcelo Bielsa stayed for several months after arriving in England last summer.
The Grade I-listed hotel boasts two golf courses, a spa, rooftop garden, indoor swimming pool, private cinema, gym, two restaurants and 300 acres of landscaped gardens and woodland.