Officers said the collision occurred at 21:20 at the crossroads with Savile Street, Parade Road and Elizabeth Place, by Helvetia School in Rouge Bouillon.
“A grey BMW driving along Rouge Bouillon struck a female pedestrian as she crossed the road. She sustained several broken bones and was transported to hospital by ambulance,” they said.
Police now want to hear from anyone who saw what happened or who may have dash cam footage.
Anyone who can help is asked to call 612612 or make an anonymous report via independent charity Crimestoppers on 0800 555 111 or using their Anonymous Online Form.