The man abandoned the vehicle and was later arrested.
Police said the woman received moderate injuries and was taken to hospital.
A witness who did not wish to be named said there was a “massive police presence” on Fairview Rd just off Steeles Lane.
He said an area of a house was cordoned off, with “heaps of police and ambulances” present.
He said people were crying and looked in shock.
A police spokeswoman said there would be a police presence while inquiries continue.