Officers were in Devonshire Gardens as part of an ongoing investigation when the car was driven at the officer.
The 36-year-old was taken to Queen Elizabeth University Hospital with serious but non-life threatening injuries.
A second man, 53, was also taken to the hospital with serious but non-life threatening injuries. He was subsequently arrested.
Detective Inspector Clark Hill, based at Govan CID, said: "Plain clothed officers were in the Devonshire Gardens area of Glasgow as part of an ongoing investigation when a disturbance happened around 5.50pm on Tuesday, July 21, 2020.
"During the disturbance, a car involved in the investigation was driven at one male officer.
"The constable, aged 36, was taken to Queen Elizabeth University Hospital with serious but non-life threatening injuries.
"A 53-year-old man was also taken to the Queen Elizabeth University Hospital with serious but non-life threatening injuries and he has been arrested.
"A 30-year-old man has also been arrested. Inquiries are ongoing."