The woman, in her 70s, was riding a mobility scooter when she was hit by a blue Jaguar whilst crossing Victoria Road at 2.38pm on December 3.
North Yorkshire Police said the woman suffered multiple fractures and was taken to hospital with "serious" back injuries; she has since been discharged.
Officers have launched an investigation and are appealing for any witnesses who are yet to come forward or anyone who saw the car before the collision.
The woman who was driving the Jaguar is assisting with enquiries and at this stage, no arrests have been made, police said.
Anyone with information is urged to contact North Yorkshire Police on 101, select option 2, and ask for PC 965 McIntosh or email [email protected]
Quote reference number: 12210254124.