Officials said 76 people were injured, including seven described as being in serious condition, the Daily Telegraph reported. About 700 people were evacuated.
Police said no one appeared to have been killed. At least 51 people were treated at hospitals, with three London buses transporting some of them.
The Gielgud Theater hosted emergency workers and their patients, the Telegraph said.
The collapse occurred as a packed house watched "The Curious Incident Of The Dog In The Night-Time." Some members of the audience said they thought the loud noise and clouds of dust as the roof began coming down were special effects for the play.
Jessica Bowie, a magazine editor, said she was unsure at first whether the roof or a balcony had come down in the historic building.
"There were people walking around covered in blood or dust," she said. "We were in the stalls at the back so we were among the first to get out. There was a huge swell of people behind us. As we were leaving, I looked at the state of the usher and he just had a look of panic and was saying 'get out.'"
Witnesses reported hearing "a strange cracking noise" about halfway through the first act, the BBC said.
Part of the dome roof of the historic building on Shaftesbury Avenue came down, officials said.
The 112-year-old Apollo Theater has seats for 775 patrons on four levels.