The incident occurred near Eddy and Cyril Magnin streets about 10:43 p.m., police said.
Pedestrians were crossing Eddy Street with the green light while the vehicle was stopped at a red light. When the light turned green, the vehicle turned northbound onto Cyril Magnin and struck a pedestrian in the crosswalk.
The vehicle then backed up and continued northbound on Cyril Magnin without stopping, police said.
The officers gave chase but could not catch up with the vehicle.
The pedestrian was hospitalized with injuries not considered life-threatening.
The vehicle was spotted later by police and impounded, however no arrests were made.