They had been checking reports of a burglary at garages behind homes in Westacre Crescent, Finchfield, when a Blue Peugeot 407 estate car was driven at them.
One of the officers, a woman, suffered serious leg injuries and remains in hospital. The other, male officer was taken to hospital with minor injuries and has since been released.
The Peugeot 407 was later recovered by police around one mile away in Windmill Crescent near Smestow School.
It is being forensically examined as detectives seek to trace those responsible.
The incident prompted the Chief Constable of West Midlands Police, Dave Thompson, to issue an appeal from his personal Twitter account.
The drama unfolded in the quiet residential road, near its junction with Limehurst Avenue, at around 12.30am on Saturday.
Residents of Westacre Crescent today spoke of their shock following the hit-and-run.
Susan James, who lives next to the garages, said: "It woke me up about 1am when I saw flashing lights and heard car doors being slammed.
"There were lots of policemen and women running up the drive to the garage block, around six police cars, an ambulance and what looked like two riot vans.
"A little later an officer knocked my door and asked if I had seen or heard anything. I asked what had happened and they said someone had been knocked over in a hit-and-run.
"There must be about 30 garages back there but only about half of them are in use. I have got one and so has my brother and there hasn't been any problems with those."
Matt Clinton, aged 28, added: "The road is quiet generally and it is a quiet area. Not a lot goes goes on around here usually."
West Midlands Police has asked anyone who saw what happened or has information to call 101 giving reference 79 04/11.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org