Several audience members were injured at Piccadilly Theatre as part of the roof crashed down into the auditorium.
Witnesses described hearing screams from audience members, some of whom later emerged from the venue covered in debris.
Emergency services were called to the packed theatre just before 8pm on Wednesday. The Metropolitan Police said a “few” people had suffered minor injuries.
Journalist Martin George, 41, who was sitting in the Grand Circle, described a a dripping noise early in the performance which may have heralded the collapse.
“About 10 minutes into the performance you could hear this slight dripping sound in the circle and people were looking around, wondering what was happening, but the play carried on,” Mr George said.
“As the minutes passed, the dripping became more frequent and it sounded like more water was coming through the ceiling, causing a few people to get up and move.
“The sound eventually got so loud that we stood up and started to leave, as we were wondering what was going to happen.
“Then, as we stood up, this huge chunk of ceiling, about three to four metres across, crashed down. There were people screaming at that point and everyone got up and streamed down the stairs.”
The London Ambulance Service, London Fire Brigade and Metropolitan Police were called to the scene, Scotland Yard said.
The Met Police tweeted: “Everyone is out of the theatre. A few people have suffered minor injuries. Road closures in place. Motorists advised to use alternative routes.”
It is not the first time a ceiling has collapsed in one of London’s theatres.
In 2013, 80 people were injured after part of the Apollo theatre’s ceiling collapsed on top of them.
More than 700 people were inside the Shaftesbury Avenue venue – which was 45 minutes into the National Theatre’s performance of The Curious Incident Of The Dog In The Night-Time – when the incident took place.
Additional reporting by PA