Officials said most of the injured were "walking wounded" with upper-body injuries, and that all are conscious and breathing.
Police and fire officials said it was too soon to say what had caused the partial collapse of the ceiling, but that a full investigation is being carried out.
Dee Stephenson said she was seated near the stage and heard the main actor shout "watch out!"
"Then you could feel the debris literally coming down on you and then I got hit on the back by a large piece," she told The Associated Press. "It was a complete dust curtain. You couldn't see."
Scott Daniels, an American tourist who lives in the Dallas area, said he'd managed to buy a last-minute ticket to the acclaimed production just before show time.
"I was lucky to get one seat that they had left over," he told The Associated Press. About 40 or 45 minutes into the show, he said, he started hearing noises — and screaming.
"I thought, maybe this is part of the play," he said. "All of a sudden, plaster starts raining down, huge hunks of plaster ... The lights went out and everything filled with dust — everybody was coughing and choking."
He said he made it out with "a couple scrapes," though he saw others with more serious lacerations.
Dust-covered theatergoers, many with bandaged heads, were treated by dozens of emergency workers in the street outside the Apollo and at a nearby theater.
City buses were commandeered to usher some of the wounded to hospitals.
Injuries ranged from head wounds to cuts and scrapes to breathing problems.
Initially, London Ambulance Service said more than 80 people had been injured. But noting that the initial situation was confusing, it later adjusted that number to say it had treated 76 patients, 58 of whom were taken to hospitals.
Of those, 51 had suffered minor injuries and seven had suffered "more serious injuries." There were no fatalities and none of the injuries are believed to be life-threatening, officials added.
The fire department said no one was trapped in the theater, explaining that rescuers had helped evacuate some theatergoers who had been trapped "by the nature of their injuries" where they had stood when the ornate plastering came down.
Chief Superintendent Paul Rickett said that "so far, we know that a number of items of masonry have fallen down from the ceiling.