"There is no suggestion at this stage that this was as a result of a criminal act, however, at this stage we are keeping an open mind," he added.
Shaftesbury Avenue, normally one of London's busiest streets and teeming with pedestrians, was completely shut down by emergency workers.
The Apollo Theatre, named for the Greek and Roman god of music and the arts, was built in 1901 and has 775 seats.
The show, which is aimed at young people as well as adults, is about a boy with Asperger's who sets out to solve a crime.
Prime Minister David Cameron said via Twitter that he was being updated regularly on the crisis. He praised the city's emergency services — who were on the scene within three minutes — for their "fast work" in helping the injured.