The incident happened at the Apollo Theatre during the West End show "The Curious Incident of the Dog in the Night-time", and comes during the week before Christmas when London's theatres are traditionally busy.
Hundreds of emergency workers rushed to the scene after the collapse but firefighters said all those trapped had been freed.
"We were called to the Apollo Theatre in Shaftesbury Avenue to reports of a ceiling collapse during a performance. We are aware of a number of casualties," the Scotland Yard spokesman told AFP.
Five people were seriously injured and taken to hospital in central London, police said. They said they were not aware of any fatalities.
AFPTV reporters saw at least one person being stretchered away from the scene. Others, including some with bandages on their heads, were being treated in the lobby of a nearby theatre.
Emergency services said they had reports that the collapse involved part of a balcony.
Pictures on social media showed people fleeing the theatre with head injuries and covered in dust.
Audience members said they had heard creaking during the performance.
Simon Usborne, a writer for the Independent newspaper, said there was a "cloud" of dust obscuring the stage after parts of masonry appeared to fall away.
"There was panic, there was screaming," he said.
Martin Bostock said he suffered a head injury after he was hit by falling debris.
"It was complete chaos in the theatre. Absolutely terrifying and awful," he told Britain's Sky News.
"I was in the lower stalls with my family in the early stages of the show.
"I think the front part of the balcony fell down. At first we thought it was part of the show.
"Then I got hit on the head.
"We got out with cuts and bruises. I think most people did."