The woman, aged in her 60s, was struck from behind in the car park of Priory Medical Group on Cornlands Road, Acomb, York.
One of her legs was left bruised and swollen as a result of the collision which happened sometime between 10am and 12pm last Tuesday (January 22).
The driver of the vehicle, a woman also aged in her 60s with short blond/grey hair, and a male passenger both got out of the car and spoke briefly to the injured woman.
A female driver of a second vehicle who witnessed the collision went to the woman's aid and took her inside the doctors surgery.
North Yorkshire Police wishes to speak to the occupants of both cars to establish the full circumstances. Anyone with information is asked to contact the force on 101 quoting reference number 12190016077.