Toronto's CBC News reports that one person was pronounced dead at the scene and at least three were injured in the accident.
Calls came in to emergency crews at around 4pm ET. One person was transported to Sunnybrook Hospital in serious condition while others assessed at the scene had minor injuries.
CP24 reported last night that one person was still trapped underneath the collapsed stage.
A spokesman for Live Nation Entertainment subsequently tweeted that the concert has been cancelled.
A post on Radiohead's Facebook page read: "Due to unforeseen circumstances the radiohead show at downsview park tonight has been cancelled. (sic)
"Fans are advised not to make their way to the venue. Refunds will be made at point of purchase."
Police have said that the park was not full at the time of the accident, but there was a significant crowd of people who had arrived early to wait for the show. The area has now been cleared by emergency crews.
Last summer saw a number of incidents at festivals involving stage collapses, with fatalities at the Indiana State Fair and the Belgian Pukkelpop music festival.