The crash happened at about 7.30pm yesterday (Saturday) on Roundhay Road, close to the junction with Roseville Road.
A Seat Leon was involved in a collision with an 18-year-old pedestrian, a West Yorkshire Police spokesman said.
He suffered suspected lower limb fractures and was taken to hospital.
The spokesman said his injuries have been described as serious but not life-threatening.
It is understood that a cordon was put in place, affecting traffic on part of the A58 on Roundhay Road, while police were at the scene yesterday.