The venue in Denman Street was packed for a performance of the Arthur Miller play Death of a Salesman.
One audience member wrote on Twitter: "Two fire crews quick to clear the area.saw one person being treated for a head injury outside".
A picture from the Twitter feed of @KBGDunn showing the hole in the ceiling at the Piccadilly Theatre.
This footage shows crowds outside the theater as it was being evacuated and actor Wendell Pierce talking to fans.
"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.
Chief executive Jon Morgan said in a statement: "We do not know yet what caused this and it is important not to jump to conclusions until more details are known".
Sky Sports pundit gives his prediction for Red Star Belgrade v Tottenham
But the statistics show that Spurs should expect anything but an easy ride when they walk out at the Rajko Mitic Stadium. The win gives Tottenham a strong hold on second place in Group B, with a four-point cushion to Red Star in third.
George said: "About 10 minutes into the performance you could hear this slight dripping sound in the [Grand] circle and people were looking around, wondering what was happening, but the play carried on".
The City of Westminster police said on Twitter: "Everyone is out of the theatre".
"Road closures in place".
In 2013, about 80 people were injured, seven seriously, after part of the Apollo theatre's ceiling collapsed on top of them. "Motorists advised to use alternative routes". The theatre had been completely evacuated, it was stated in the police notice.
Describing the scene interior, journalist Martin George, 41, who became once sitting within the Immense Circle, mentioned there had been screams coming from the viewers as share of the ceiling got right here crashing down.
He said that before the collapse there had been a steady drop of water "which turned progressively into a stream" - although it was not raining at the time - and said there was some panic when the ceiling fell in.