The 14-year-old, who was riding a bike, suffered leg, head and shoulder injuries during a collision with a black Ford Mondeo on Harcourt Drive, Harrogate, close to the junction with Kingsway at 1pm on Friday (August 5).
He was taken to Harrogate District Hospital where his condition is described as comfortable by police.
Officers are appealing for the woman who stopped at the scene to help the injured boy, and any other witnesses, to come forward.
The woman stayed with the boy until his parents arrived at the scene. Witnesses are asked to contact North Yorkshire Police on 101, select option 2 and ask for Traffic Constable Rob Roberts of Harrogate Roads Policing Group, quoting reference number 12160140826.