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The Roar had been set to host Palace in Townsville on July 11 and West Ham on the Gold Coast four days later before the Premier League outfits clashed in Brisbane on July 18.
However, uncertainty caused by the pandemic has forced cup organisers to find another date.
"It is a real shame that we will no longer be able to make it over to Queensland this summer, however, it is the right decision to postpone given the circumstances," West Ham manager David Moyes said.
"We hope the tournament can be rearranged at a later date once things are back to normal, and we look forward to visiting Australia in the future."
Crystal Palace chairman Steve Parish said the club would do everything it could to play in Queensland next year.
"It is bitterly disappointing not to be able to make the club's landmark trip to Queensland this July for everyone here at the club," he said.
"We will do everything we possibly can to try to rearrange the tour for 2021, once things become clear with the Premier League schedule for the remainder of this season, and next year's provisional timings too."
Roar CEO David Pourre said Brisbane "still look forward to welcoming two of England's most historic clubs to Queensland at a later date."