The incident took pace at a retail park on Wilmslow Road, Cheadle, on Saturday night, January 25, leaving the officer with serious injuries.
Greater Manchester Police received reports of people acting suspiciously inside a vehicle in the car park.
As the responding police officer walked towards the vehicle, it drove off at speed towards her and hitting her.
She remains in hospital and is being treated for her injuries.
Chief Inspector John Picton of the Stockport district said: “This incident is truly shocking, and shows how quickly situations our frontline officers attend can escalate. There is absolutely no explanation as to why this incident needed to end the way it did.
“Our officers go to work every day to provide an outstanding service to the communities they serve, and achieve fantastic results in situations that are often challenging.
“Assaults on our officers are completely unacceptable and won’t be tolerated. In this case, the officer suffered serious injuries.
“Our investigation is continuing, and the officer is being supported by all of us at the Stockport district. She is recovering well.”