The Metropolitan Police said a "few" people had suffered minor injuries and that emergency services remained on scene.
A picture from the Twitter feed of @KBGDunn showing the hole in the ceiling at the Piccadilly Theatre.
Wendell Pierce, who plays Willy Loman in the show - which only opened on Monday - apologised to those who had been evacuated.
"We apologise and we are glad that no one is hurt and I ask you all to come back and see our production", he said.
We are sorry to confirm that at 8pm this evening during a performance at the Piccadilly Theatre a section of plasterboard fell from the upper rear circle.
"On twitter, Laura Kate Jones described the incident as 'terrifying", saying people were "running and screaming to get out".
It is not yet known whether the Piccadilly Theatre has a suspended fibrous plaster ceiling, and no details about the cause of the collapse have yet been confirmed. 'Facet road closures in feature. "Around 1,100 people evacuated the theatre before we arrived".
'Motorists informed to spend different routes'.
"The performance was immediately stopped and the theatre safely evacuated".
Writing on social media, one audience member claimed the ceiling collapse started "with some dripping" that "increased" until it "all caved in".
Journalist Martin George said there were screams coming from the audience as part of the ceiling came crashing down.
In December of 2013, the ceiling of London's Apollo Theatre partially collapsed during a performance of The Curious Incident in the Dog in the Night-Time.