The collapse happened at the Apollo Theatre on Shaftesbury Avenue at 8:15 p.m. (2015 GMT; 3:15 p.m.) during a performance of "The Curious Incident Of The Dog In The Nighttime" at the height of the Christmas holiday season.
"Complete chaos" erupted in the theater as the debris rained down, said Martin Bostock, who came with his family to see the show, which is based on the best-selling novel by Mark Haddon.
"At first we thought it was part of the show," he told Sky News. "Then I got hit on the head."
Witnesses said audience members were screaming "Get out! Get out!" as they fled the theater and were shaking with fear when they reached the street outside.
"Within an instant, the entire roof caved in," another man told the BBC.
A passing public double-decker bus was commandeered to transport some of the injured to a hospital.
Police said they weren't aware of any fatalities "at this early stage," and that those who were seriously injured had been taken to hospitals following the collapse.
Dozens of "walking wounded" were treated at a nearby theater, police said, while the fire department reported that all those who had been trapped in the Apollo have been rescued. More than two dozen ambulances and eight fire trucks were sent to the scene. Shaftesbury Avenue, normally one of London's busiest streets and teeming with pedestrians, was completely shut down.
London was hit by a strong thunderstorm about 7 p.m. (1900 GMT; 2 p.m. EST) that dumped heavy rain on the city, but it wasn't immediately clear if that was related to the collapse.
The Apollo Theatre, named for the Greek and Roman god Apollo, god of music and the arts, was built in 1901 and has 775 seats. The London fire department said it thought around 700 people were in the theater at the time.
On its website, the theatre warned that its balcony was one of the steepest in London "so avoid if you have trouble with heights."
