A scaffold structure 15 metres above the main stage in Donsview Park, Toronto, collapsed at 4pm. No strong winds or adverse weather was reported.
Around 40,000 people were expected for the sold-out gig. Fans were told not to make their way to the venue, and that all tickets would be refunded.
A statement on Radiohead’s website said the band have been "shattered by the loss" of Johnson.
"He was a lovely man, always positive, supportive and funny; a highly skilled and valued member of our great road crew. We will miss him very much."
The incident comes less than a year after two stages collapsed at Belgium's Pukkelpop music festival, killing five and injuring at least 50 people. It also follows the disaster at the Indiana State Fair in Indianapolis after metal scaffolding fell onto a crowd of fans and workers, which claimed seven lives.
Pat Fellows, health and safety director at Crewsaders, told Event the temporary structure industry that provides concert staging needs to learn from this incident."It is clear that either there was no safe system of work put in place or it was completely disregarded. It is our duty as managers to provide safe guidelines of work for our crew and then ensure those methods are followed."
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To read more from us on stage safety check out our special report in October 2011, and on crowd safety in the April 2012 issue. You can get hold of the print magazine by subscribing here.