The man was knocked from his bicycle on the A65 between Clapham and Austwick, but the driver of the white van involved in the collision failed to stop at the scene.
The cyclist was taken by ambulance to Lancaster Royal Infirmary with a suspected back injury.
Police are now appealing for anyone with dash-cam footage of the van to come forward about the incident, which happened at about 1.35pm on Thursday (September 27).
A spokesperson for North Yorkshire Police said: "If you can help, please contact North Yorkshire Police on 101, select option 2, and ask for David Burgess. You can also email [email protected]
"Please quote the North Yorkshire Police reference number 12180180922."