The incident happened, at about 9.15pm on Monday 16 November).
Officers spotted a grey Audi RS driving erratically on the Black Country Route and stopped the vehicle at lights at the junction of Millfields Road and Manor Road.
As one of the officers approached the vehicle it accelerated towards him, hitting him and throwing him across the bonnet before driving off in the direction of Bilston town centre.
During searches, officers found the Audi abandoned on Mill Street at about 21.55 GMT and it has been seized for forensic investigations.
The injured officer, who was treated at the hospital for minor injuries to his leg, has been discharged and is now recovering at home.
It is understood there were two men in the Audi and as police investigations continue detectives are keen to hear from anyone who may have seen the incident or seen 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 dashcam footage of the incident or who may have seen anyone fleeing from the Audi to contact us.”
Anyone with information can contact police online via live chat, or by calling 101, and quoting crime number 20WV/282593X/20.