Eyewitnesses described "chaos and panic" last night as parts of the Apollo theatre "began to crumble down" around them.
Masonry and ornate plaster from the Grade II listed theatre plummeted on to the stalls below, dragging a section of the balcony with it, striking members of the packed audience and filling the theatre with clouds of thick dust.
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 members of the audience started screaming as it appeared parts of the ceiling caved in.
A district surveyor from Westminster City Council carried out a structural assessment of the building during the night to ensure it was safe, and is expected to report on preliminary findings at 9am, the BBC said.
Nimax Theatres, which owns the Apollo, described the incident as "shocking an upsetting", while Simon Stephens, the show playwright, wrote on Twitter: "Thank you for your messages on this sad and strange night."
Police commandeered three London buses to take the injured to hospital, many of whom were described as "walking wounded" and were left bloodied and bandaged, and a makeshift triage was set up at the Gielgud Theatre.
London Ambulance Service said it treated 76 patients, of whom 58 were taken to four hospitals.
Of those, 51 had suffered minor injuries and seven more serious injuries. There were no fatalities.
Eyewitnesses spoke of hearing a loud "creaking" which some initially thought was part of the show.
Theatre-goer Khalil Anjarwalla said he, his heavily pregnant wife and her parents managed to escape from the theatre safely after "kilos of concrete plummeted from the ceiling".
Business owner Mr Anjarwalla, 29, said: "I was in the upper circle with my family when, about 45 minutes in, people started shouting and screaming.
"Within an instant the whole roof seemed to come down.
"We saw a lot of people completely covered in dust - I could hardly breathe.
"We had to get out, calmly. I remember thinking the cloud, the dust."
Mr Anjarwalla, who was visiting his in-laws with his English wife, Aliya, said: "The actors just seemed to run from the stage. They had obviously seen what had happened.
"We initially thought it was part of the show. Thankfully we are all OK. My wife is seven months' pregnant but she is OK. We feel very blessed."
He said some people seemed to be "cut quite badly".
Photographs from inside the theatre showed heavy beams and wood strewn across seats, which were coated in debris and dust.
Incident commander Maria Smith, who was one of the first on scene at around 8.10pm, said: "When I arrived it was dark and extremely dusty and people were lying on the floor of the theatre.
"We very quickly set up a casualty clearing area in the foyer of the theatre and the walking wounded were assessed and treated there for injuries such as cuts and grazes, breathing problems and head injuries.
"All the staff involved did an excellent job to help ensure that people received medical attention and those who needed further treatment were taken to hospital."
Chief Superintendent Paul Rickett said: "So far we know that a number of items of masonry have fallen down from the ceiling.
"There is no suggestion at this stage that this was as a result of a criminal act, however, at this stage we are keeping an open mind."
Eight fire engines, specialist rescue workers and more than 50 firefighters worked alongside hundreds of police officers at the scene.
Emergency crews said there was no evidence of anybody being stuck inside the building.
Kingsland station manager Nick Harding, from London Fire Service, said: "A section of the theatre's ceiling collapsed on to the audience who were watching the show. The ceiling took parts of the balconies down with it.
"Firefighters worked really hard in very difficult conditions and I'd like to pay tribute to them. They rescued people from the theatre, made the area safe and then helped ambulance crews with the injured.
"In my time as a fire officer I've never seen an incident like this. I imagine lots of people were out enjoying the show in the run-up to Christmas. My thoughts go out to all those affected."
Sean Walsh, who was visiting the show with his girlfriend, said they were sitting in the balcony when they first spotted a group of people below them shouting to leave the theatre immediately.
Mr Walsh, 41, from north London, said: "We were right up in the gods and a couple in the group below just said 'Go!'
"We thought they were just leaving because maybe they were bored, and my girlfriend thought maybe they had seen a mouse.
"But then the whole of the ceiling just came down."
He said people in the balcony filed out of the theatre calmly, but added: "It was difficult - you could hardly see the seat in front of you, due to the dust."
One 29-year-old, who would only give his name as Ben, said: "We got out fairly quickly, I think everyone was quite panicked."
In a statement, a Nimax spokesman said: "Our thoughts are with the audience and staff who were in the theatre and their families.
"We're very grateful to the emergency services for their tremendous work and to our staff who helped with the evacuation.
"We will continue to co-operate fully with the authorities to establish exactly what happened."
Council leader Philippa Roe said: "We are obviously shocked to hear the news and our immediate concerns are with the people that have been injured. Our officers are on site and they will help emergency services wherever they can."
Ms Roe later told BBC London 94.9 that other buildings would be checked to ensure there was not a possibility of a recurring problem.
Mark Haddon, who wrote the award-winning murder mystery on which the play is based, took to the social networking site to add: "It's been horrifying sitting here watching what has been happening at the Apollo this evening. I'm hugely relieved that no-one has died.
"I hope that those who were seriously injured are OK. I'm sorry, too, that so many people went through such a terrifying experience."
Prime Minister David Cameron paid tribute to rescue crews, writing on Twitter: "I've been updated regularly on the Apollo incident. I'm grateful for the fast work of the emergency services in helping the injured."
Mayor of London Boris Johnson added last night: "Thank you to everyone involved in the emergency operation at the Apollo theatre tonight - incredible response in very difficult conditions."
The theatre is now sealed off and the search of the building "now complete" London Fire Brigade said.