The man was driving a Ford Ka when the vehicle failed to stop for police in Bramley at 10.20pm last night.
Cannabis factory in Beeston raided by policeOfficers gave chase but lost the car in Kirkstall Hill.
Shortly afterwards it crashed into a Ford Fiesta in Burley, injuring the driver.
The Ka driver and passengers ran from the scene.
West Yorkshire Police said:-
"At 10.20pm last night a Ford Ka failed to stop for police in the Bramley area of Leeds and was pursued.
"The vehicle made off from officers and was lost in the vicinity of Kirkstall Hill.
"A short time later the vehicle was found to have been involved in a collision with a Ford Fiesta in Burley Road at the junction with Cardigan Road.
"The occupants of the Ford Ka ran off from the scene.
"The driver of the Fiesta, a 55-year-old man, was taken to hospital with injuries that were serious but not life threatening.
"A 21-year-old man was later arrested on suspicion of drink driving and failing to stop for police. He was taken to hospital for treatment to injuries that were not considered life threatening."