Authorities said after the stabbing, the officer then shot the suspect, possibly in the back.
The incident happened at the Hollywood Palladium on the 6200 block of Sunset Boulevard.
Two off-duty officers were leaving a concert featuring the band "A Day to Remember," according to the Los Angeles Police Department.
There was an altercation with a man armed with a knife. One officer withdrew his weapon and ordered the man to drop his knife.
Both the officer and suspect were treated at a hospital and released. The suspect is still in custody.