The shooting occurred at about 9:10 p.m. at Tolin's Liquors at 7101 International Blvd., according to Oakland police spokesman Jeff Thomason.
Polk, an Oakland resident, was transported to a local hospital, where he died, Thomason said.
The officer, whose name has not been released, wasn't injured. An investigation into the shooting is ongoing.
Anyone with information regarding the incident is asked to call the Oakland Police Department Homicide Section at (510) 238-3821.