The incident happened outside Northwood Park Primary School in Bushbury during the morning school run on Thursday.
Two men were fighting before one of them got into a BMW and drove into the other man, West Midlands Police said.
The man hit by the car was treated by paramedics and taken to hospital.
A spokesman for West Midlands Police said: "Police were called to disorder in Collingwood Road, Bushbury, Wolverhampton, just after 8.50am.
"Two men were involved in a fight until members of the public intervened.
"One of the men then got into a white BMW 3 Series and drove at the other man, hitting him.
"He was taken to hospital with injuries which are not believed to be serious.
"Enquiries and anyone with information can contact police via Live Chat at www.west-midlands.pnn.police.uk between 8am and midnight or call 101 anytime. Quote crime reference number 20WV/245606V/19."
A West Midlands Ambulance spokesman added: "We were called at 8.52am called to reports of an altercation outside Northwood Primary School that's resulted in a pedestrian being in a collision with a car.
"We sent one ambulance to the scene and treated a man in his 30s for potentially serious injuries at the scene before taking him to hospital."