The collision took place in Robin Hood Road, Edenthorpe at around 9pm on Saturday evening, involving a Golf and a Ford Focus vehicle.
Police, ambulance and fire services were sent to the scene.
A South Yorkshire Fire and Rescue spokesman said the man driving the Ford Focus had to be removed from his vehicle by firefighters.
The man driving the Golf was arrested at the roadside by police.
Both men were taken to hospital for checks. The extent of their injuries is not yet known.