The victim was hit in Knaresborough earlier this week.
The road was closed for repairs but the driver of the car was allowed through when he told the work crew he was picking up a child.
When he tried to make the return trip he was told that he couldn’t drive through the site by one the construction workers.
Police said the driver refused to follow the diversion and drove through the site hitting the construction worker.
The 18-year-old man who had been working on the road, from County Durham, was taken to Harrogate District Hospital with a suspected broken leg. He has since been discharged.
Police are now appealing for witnesses after the driver failed to stop.
The driver is described as being white and aged in his 60s.
TC Dave Lever, of North Yorkshire Police’s Roads Policing Group, told the Harrogate Advertiser: “If you are the driver of the vehicle involved in this collision, it is possible that you are unaware that a collision occurred, and I urge you to come forward straight away so that I can take your statement.”