The incident happened on Cranmer Bank, Moortown at 6.30pm today.
Fire crews had to remove the driver of the car from the vehicle after the collision with a bus.
A West Yorkshire Fire and Rescue Service spokesman said: “The male occupier of the car suffered trauma to his arms and legs and was extricated from the vehicle by fire service personnel and transported to hospital by ambulance.”
A passenger was treated at the scene by paramedics and the bus driver was also taken to hospital as a precaution.
Fire crews from Moortown and Cookridge attended the scene this evening.