South Yorkshire Fire and Rescue said emergency services were alerted to the incident in Stainforth Road, Barnby Dun, at 2.40am.
A spokeswoman said firefighters had to release the woman from underneath the car.
She was treated by paramedics at the scene.
Police closed the road, with traffic diverted along Bramwith Lane, while the incident was dealt with and investigations were carried out at the scene.
The extent of the woman’s injuries have not been released.