The accident happened on Dewsbury Road in Leeds at around 1.45am on Sunday by the Kasa store.
The driver of a grey Vauxhall Insignia reported a road traffic collision and began administering first aid to the injured party, before he got up and left the scene.
A police helicopter was deployed to look for the man but he was not traced.
The man, who is thought to have head injuries, is described as a white male, 5ft 8, brown hair, blue jeans and wearing a bomber jacket. He is thought to be aged in his 20s
It is thought the missing male walked along Dewsbury Road towards Leeds city centre.
Detective Inspector James Entwistle of Leeds CID, said: “We are urgently looking to trace this male as a witness has described him as having a significant head injury. That, combined with the damage to the vehicle, leads us to believe he needs immediate medical attention and we urge anyone who was in the area at the time or that knows someone who may have been to contact us.
“Or if you saw the missing man around this time in the area please call us as we are still trying to establish more information about him and where he went.”
Anyone with information is asked to call 101 quoting reference number 194.