The victim of the assault, a 35-year-old man from the Goole area, was using the crossing when a black Volkswagen Golf approached the crossing and stopped.
The victim and his girlfriend continued across the crossing. The driver of the Golf then got out of his vehicle, walked after the couple and struck the man who fell to the floor banging his head and losing consciousness.
The victim was taken to York District Hospital with serious head and facial injuries where he remains in a stable condition.
A woman passenger who got out of the vehicle after the assault was left behind when the suspect drove off, she left the scene on foot.
The street was busy with pedestrians at the time of the incident and members of the public who saw what happened went to the aid of the victim.
Police would like to speak to anyone who witnessed the incident or who has any information which can help the investigation.
Detective Sergeant Fiona Wynne said: "This was a violent and unprovoked assault in a busy shopping thoroughfare. The victim received serious head injuries and the whole incident was a horrific experience for his girlfriend who was present when the assault took place.
Anyone with any information is asked to call North Yorkshire Police on 101, select option 1 and quote incident number 12120000852.