Bell Hill Apartments caretaker Izaak Auperle, of Dunedin, said CCTV footage showed a woman trying to get through the gate of the car park in Moray Pl, between Princes and Burlington Sts, about 12.30pm on Saturday.
She got part-way out of her car to swipe her access fob before getting back in, Mr Auperle said.
Before the gate was fully open, the vehicle suddenly sped out of frame.
"She just hit the accelerator somehow," Mr Auperle said.
The car hit the brick wall on the right of the alleyway, before overturning, he said.
The gate was bent in the crash, but had been restored to working order by yesterday afternoon.
The crash must have been frightening for the woman, Mr Auperle said.
A Hato Hone St John spokesman said an ambulance and a rapid response vehicle attended and the woman was taken to Dunedin Hospital with moderate injuries.
A Fire and Emergency New Zealand spokesman said two crews, from Willowbank and Dunedin City stations, attended the incident and the woman did not need to be extricated.
Police also attended. — Additional reporting Reuben McDougall
