Everyone is out of the theatre. A few people have suffered minor injuries.
The London ambulance service, London fire brigade and Met police were called to the scene and road closures are in place around the theatre, Scotland Yard said. "Motorists advised to use alternative routes".
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. The theatre had been completely evacuated, it was stated in the police notice.
It is not the first time a ceiling has collapsed in one of London's theatres.
The production features Hollywood actor Wendell Pierce and one witness, Tracy De Groose, said the star came out to check everyone was okay.
A statement from ABTT said it was "very concerned to learn of the events at the Piccadilly Theatre...and our thoughts are with all those who were involved in the incident".
He said there was water dripping before the collapse.
A number of audience members praised the theatre staff for the speed with which they evacuated the building.
"Then, as we stood up, this huge chunk of ceiling, about three to four metres across, crashed down".
"Thank you @WendellPierce for coming out to check everyone safe".
'There had been folk screaming at that level and all americans got up and streamed down the stairs'.
The City of Westminster Police said they rushed to the scene after reports of a "ceiling collapse around 19:59hrs". "We apologize and we're glad that no-one's hurt".
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.