Radiohead say their lighting rigs and other parts of their stage show were destroyed in the Toronto stage collapse that killed the band's drum technician and injured three others.
The British rock act, due in New Zealand for a one-off show on November 6, said the damage had forced them to rescedule nine appearances in Switzerland, Germany and Italy.
The changes did not affect the timing of the Auckland show at Vector Arena.
The band were scheduled to perform in Toronto when the stage collapsed before opening act Caribou were set to begin.
"It was like fireworks went off and then boom, the stage just crumbled to the ground in a matter of seconds," said fan Mike Kensey. "I had never really seen anything like it."
In a statement, Radiohead said they needed time to rebuild their "unique" live show.
"As you will probably have heard the roof over the stage collapsed at our show in Toronto killing crew member Scott Johnson and injuring three other crew members," Radiohead said in a statement on their website.
"The collapse also destroyed the light show - this show was unique and will take many weeks to replace. The collapse also caused serious damage to our backline, some elements of which are decades old and therefore hard to replace.
"Whilst we all are dealing with the grief and shock ensuing from this terrible accident there are also many practical considerations to deal with & consequently we have to try and reschedule (some) shows.
"We aim to announce the new dates for these shows on Wednesday 27th of June and will also supply information on how to obtain refunds on tickets if you cannot come to the show on the new date."
Radiohead said they would resume their world tour at the Les Arenes Nimes, Bilbao BBK festival and Lisbon Optimus Alive festival and "will make every effort to offer the fans the very best show possible under the circumstances".
In an earlier statement, Radiohead said they were "shattered" by the stage collapse and death of "friend and colleague" Scott 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. Our thoughts and love are with Scott's family and all those close to him."
- Herald online