The 61-year-old was taken to Leeds General Infirmary following the accident on Kirkstall Road near the junction with Viaduct Road around 8.20am. He was pronounced dead a short time later.
The driver, 30, is in custody on suspicion of causing death by dangerous driving.
Sergeant Carl Quinn, of the Major Collision Enquiry Team, said: “We would like to hear from anyone who witnessed the incident itself or who saw the circumstances leading up to it.”
Meanwhile police are appealing for information following the death of 72-year-old Rosemary Crosland who died in a collision with a car while walking her dog in Huddersfield, yesterday morning.
The accident happened at 7.55am on the A649 New Hey Road, Outlane and involved a silver Peugot.
Mrs Crosland was pronounced dead at the scene and her pet was also fatally injured.
Police issued an appeal today and asked anyone who witnessed the accident to call them on 101.