It happened in the 2100 block of McCarty near Kerr in east Houston.
Officials said two officers in separate cruisers were responding to a call when a third driver collided with them.
Police believe that driver's headlights were off.
One officer was hurt, but it is unclear how serious her injuries are. She was transported to Memorial Hermann Hospital.
The driver of the car took off on foot from the scene, but police caught him. He was taken to an area hospital as well with unknown injuries.
Investigators believe alcohol was a factor. There is no word yet on charges.