Police were called just before 8 pm (1959 GMT) to the West End theatre where American actor Wendell Pierce was starring as Willy Loman in a production of the 1949 play.
"Everyone is out of the theatre. A few people have suffered minor injuries," police said in a statement. London Fire Brigade said 1,100 people had been evacuated after a section of plaster fell from the ceiling.
"I did not mean for it to go like this," Pierce, known for his work in the TV show "The Wire" and the 2014 film "Selma," told theatregoers in a video posted on Twitter.
"I'd like to thank you all for safely evacuating. We apologise and we're glad that no-one's hurt."