The crash happened as the man, 80, was walking along Pateley Bridge High Street at about 11.30am on Saturday.
He was knocked to the ground after being hit by a passing car close to the pharmacy in the street, North Yorkshire Police has said.
The motorist failed to stop.
The victim was treated by ambulance staff at the scene, before being transferred to Harrogate District Hospital.
Police have today issued an appeal urging the driver of the car to come forward.
Anyone with information is asked to contact police on 101, quoting reference number NYP-13012018-0149.