The 30-year-old suffered a leg injury when the car struck her as she tried to stop the vehicle from being taken.
It was stolen from Amersall Crescent, Scawthorpe, at 8am yesterday.
South Yorkshire Police said the car was then involved in a collision with a parked car in Springcroft Drive, Scawthorpe.
A South Yorkshire Police spokesman said: "The man who reportedly stole the car has been described as aged between 20 and 30-years-old, wearing dark tracksuit bottoms and a green T-shirt.
"The 30-year-old woman, who was hit by the car, received an injury to her leg in the incident.
"Police are currently investigating both of the incidents and would like to speak to anyone who may have been in the area at the time."
Anyone with information should call South Yorkshire Police on 101.