It happened on Tadcaster Road junction with Knavesmire Road at 10.45pm on Tuesday, March 5.
The black estate car, which police believe is a taxi, crashed into the man and then drove off, leaving him injured at the scene.
Emergency services arrived and took the man to the hospital.
He is now recovering at home from slight injuries.
Police have released CCTV images of the car and are urging the driver to come forward immediately.
If you were the driver, or if you have any information that could assist the investigation, contact North Yorkshire Police on 101, select option 2, and ask for Dave Ellison. You can also email [email protected]