It happened at the Fuerzabruta show at the Roundhouse in Camden on Friday night.
Eyewitness Steve Johns, 68, said: “The sail collapsed on to technicians and members of the public below.”
A Roundhouse spokesman said the incident was “extremely regrettable” and it was investigating.
Three people were treated for minor injuries by London Ambulance and taken to the Royal Free Hospital.
A spokeswoman for the Roundhouse and the Fuerzabruta show said a performance was still planned for Saturday night, but the scene during which the incident occurred would be omitted.
Fuerzabruta’s website describes the show as a “mind-blowing, heart-pounding international theatrical experience”.
It is described as a standing show where the audience are encouraged to move around the venue as acrobats leap and perform on moving set pieces spinning above the crowd.
Photographer Mr Johns, who was at the performance with his daughter and son-in-law, said 30 minutes into the performance “the sail which was spinning above the crowded floor on which acrobats were performing, collapsed on to technicians and members of the public below.
“People were trying to get out from underneath. Fortunately, due to the efficient security service and the calm of crowd, the worst was avoided.
“They have since emailed my daughter and said we will be offered reimbursement or the chance to see another show. But she said she wouldn’t go again.”
A Roundhouse spokesman said “a piece of moving stage equipment on which two artists were performing suffered a technical failure and fell slowly into an area where audience members were standing.
“The equipment was brought in for the production and was not part of the Roundhouse structure.
“The show was stopped and the performance space was cleared immediately.”
The spokesman added: “The Roundhouse is committed to the safety and wellbeing of its audiences and undertakes rigorous risk assessments for all of the shows that take place here.”
London Ambulance said it treated one person for a facial injury, one for an ankle injury and one for concussion.
The Argentine acrobatic show premiered in Buenos Aires in 2005 and has since been staged across the world.
It returned to London in December for 100 shows and is due to run until March.