West Yorkshire Police were called just after 1.15am to reports of a collision on Armley Road, close to the junction with Pickering Road, in Armley.
Police said a blue BMW 116i and a white Toyota Auris had collided near AMT Vehicle Rental.
A spokeswoman said one car had overturned and the second was blocking the road.
She said one man, the driver of one of the cars, had been taken to Bradford Royal Infirmary for treatment to what were believed to be minor injuries.
It is believed that two others fled the scene and may have been injured.
The spokeswoman said the vehicles had been recovered before 9am.