As shocked tourists looked on,
The LAPD posted photos on Twitter showing the knife officers said they recovered at the scene, saying it belonged to the man they shot.
The department also urged witnesses to the incident to call police.
Police said the shooting occurred about 7 p.m. after LAPD's Hollywood Division received a report of an assault with a deadly weapon.
The suspect was taken to the hospital in critical condition, police said.
No officers were injured in the incident.
The shooting came as tourists and others were milling around the popular entertainment area.
"All I heard is just a bunch of gunshots, it sounded like a rifle. I thought I was about to get caught up in a shootout. Everyone was scattered. And then I realized there were police. They were posted up over a man that was lying on the ground bleeding," witness Jordan white told KABC-TV.