The band was not onstage at the time, but one person was killed and three others were injured in the collapse. The concert, whose gates were scheduled to open at 5 p.m., has been cancelled.
Toronto fire captain Mike Strapko told CNN that a "scaffolding-type structure collapsed" some 40 to 60 feet above the main stage area as the victims were setting up for the concert around 4 p.m. There were no strong winds or other dangerous weather conditions at the time.
A statement on Radiohead's website says that tickets will be refunded, and advises fans not to make their way to the venue.
The person killed by the falling structure is reported to be Radiohead's drum technician, Scott Johnson.
The accident comes after a number of recent stage collapses at high profile shows raised concerns about safety at concerts. Seven people were killed at the Indiana State Fair last August when high winds knocked down scaffolding and speakers, and just last Saturday, the Electric Daisy Carnival in Las Vegas was shut down by windstorms, forcing the cancellation of some headlining sets.
"The insurance companies that really concentrate on the entertainment industry are taking a harder look at events they're insuring," said Peter Tempkins, a Nashville insurance agent for outdoor festivals and tours including Bonnaroo and the Warped Tour. "They're taking a harder look at staging, engineer sign-off, weather monitoring, security plans, emergency plans. There's a lot of guessing going on right now on what happened up in Canada, there are a lot of rumors going on right now. The only thing that's certain to be right is it had nothing to do with weather."