It happened at around 8.50am on Sunday 26 January when the Mini, which was travelling from Starbeck towards Harrogate, left the road near Lookers Ford garage and collided with a 58-year-old man.
The Mini, which has no registered keeper, came to rest on the pavement and the driver left the scene of the collision, leaving the car behind.
The injured pedestrian was taken to Leeds General Infirmary with serious injuries, where they currently remain.
The driver of the Mini, anyone who can help identify them and anyone who witnessed the collision or saw the Mini before it collided with the pedestrian, is asked to contact North Yorkshire Police on 101, select option 2 and ask for Traffic constable Steve James, email Steve.James117@northyorkshire.pnn.police.uk
Please quote incident number 12200014610 when passing on information.