The venue in Shaftesbury Avenue was packed for a performance of The Curious Incident Of The Dog in the Night-Time, BBC reported.
Eyewitnesses heard "a crackling" noise before the collapse at about 20:15 GMT. Theatre-goers left covered in debris.
The Apollo's owner described it as a "shocking and upsetting" incident and an investigation was underway.
A total of 51 people were taken to hospital but there were no life-threatening injuries.
Prime Minister David Cameron lauded the emergency services and arrived at the scene within minutes of the collapse. He tweeted of his gratefulness for the fast response by the emergency team.
"Close to 25 ambulance crews, an air ambulance rapid response team, eight fire engines and more than 50 firefighters were involved in the rescue," said a report by BBC.