The 21-year-old man was travelling north on the A19 between Chapel Haddlesey and Burn, at about 7.50 last night.
A North Yorkshire Police spokesman said a Vauxhall Astra which was travelling in the opposite direction, tried to overtake a tractor when it was in collision with the moped.
The moped rider was taken to Doncaster Royal Infirmary for treatment to a back injury, and the police spokesman said a large number of motorists who were in traffic behind the tractor could provide vital information to the investigation.
A female driver of a large people carrier did stop at the scene, but did not leave her details, and officers have also appealed for her and the driver of the tractor to contact them as soon as possible.
Anyone who can help officers with their inquiries should contact North Yorkshire Police on 101, email firstname.lastname@example.org or phone Crimestoppers, anonymously, on 0800 555111.