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."