The officer was thrown over the bonnet of the grey Audi RS as police tried to stop the vehicle in Bilston last night.
It is believed two men were inside the car.
No arrests have yet been made but West Midlands Police has appealed for any witnesses to come forward.
The officer suffered minor leg injuries and was taken to hospital. He has since been discharged and is recovering at home.
Officers first saw the car driving erratically on the Black Country Route.
They tried to stop vehicle at a set of traffic lights, at the junction of Millfields Road and Manor Road, in Bilston, at about 9.15pm.
But the car accelerated towards the officer as he approached the vehicle and hit him, throwing him over the bonnet, before driving off towards Bilston town centre.
The Audi was founded abandoned on Mill Street at about 9.55pm following a search of the area. It has since been seized for forensic investigations.
Detectives are keen to hear from anyone who saw the incident or anyone leaving the Audi in Mill Street.
Detective Sergeant Louise Stafford, of Force CID, said: "It is through pure good fortune that this officer was not more seriously injured.
"As an officer approached the car, they were deliberately driven at and he has gone over the bonnet - the Audi then drove away leaving the officer on the ground.
"We'd urge anyone who was in the area at the time and may have dash cam footage of the incident or who may have seen anyone fleeing from the Audi to contact us."
Anyone with information can contact police by live chat on the force's website, or by calling 101, and quoting crime number 20WV/282593X/20.