The female officer was struck after she attended a row between a man and a woman.
The crash happened in Hatherton Street close to the town’s bus station.
She had been with a colleague from the Safer Travel police team when the crash happened.
Routes around the station were blocked as police dealt with the aftermath.
She suffered serious injuries following the ‘domestic incident’ at around 9am today and is currently being treated in Walsall Manor Hospital.
West Midlands Ambulance Service said the officer was treated for rib and hip injuries.
A second patient, who was a bystander and also a woman, was treated for the effects of shock but did not require hospital care.
The car was recovered shortly after in Bloxwich and West Midlands Police has confirmed investigations are ongoing in efforts to trace the offender.
A West Midlands Police spokesperson said: “Anyone with any information is urged to contact West Midlands Police either via Live Chat at west-midlands.police.uk between 8am to 9pm, call 101 anytime or contact Crimestoppers anonymously on 0800 555 111 quoting log number 483 of 6/9/18.”