The vehicle is described as a green Cadillac with an Indiana license plate.
Police said they found a car with a broken windshield blocks from the scene that matches that description.
The officer, who was taken to Advocate Christ Medical Center in Oak Lawn in "stable" condition, may have a broken leg and injuries to his face.
His injuries are not life-threatening, according to police.
The Gresham District officer, 38, was standing outside his squad car in the 7900 block of South Wabash Avenue about 12:30 a.m. when he was struck by a vehicle, police News Affairs Officer Amina Greer said.
Witnesses said they saw the officer's body on the side of the road after he was hit by the car.
The officer's name has not been released.
Major Accidents Investigation Unit is investigating the crash.
The Sun-Times Media Wire contributed to this report.