The royal-blue Mazda Sport had been travelling away from Halifax when it left left Rochdale Road at about 10.45pm yesterday.
The driver, a 44-year-old woman, was seriously injured and remains in hospital.
Police would like to speak to anyone who saw the car leaving the road or the car driving in the area at the time of the incident.
Anyone with information can contact the Safer Roads Western team on 101, quoting log number 262 of 20/8.