Officers received a call about an assault with a deadly weapon around 4:30 p.m. Monday in an underground garage at the intersection of Wilshire Boulevard and Grand Avenue.
The suspect allegedly had gotten into a dispute with a parking attendant, witnesses told police. Police arrived and confronted the man.
"When he (the officer) went downstairs, he was confronted by the suspect, who failed to cooperate with the officer's commands, and an officer-involved shooting occurred," said Sgt. Barry Montgomery, a spokesman for the Los Angeles Police Department.
The man was rushed to the hospital in critical, but stable condition. Police did not say if the weapon was recovered from the scene.