Wurundjeri elder Aunty Joy Murphy Wandin said she was informed on Friday afternoon by the club she was no longer required to address the crowd at AAMI Park before the match.
The Storm held its annual Anzac Day commemorations before the clash with South Sydney, kicking off at 8.10pm.
Murphy, who has performed the Welcome to Country at Melbourne events for years, said the Storm then reversed its position, apologised, and asked her to continue with her ceremony as originally planned.
Two First Nations groups were also scheduled to perform, but after the confusion they all decided to cancel their performances.
"We were all just dumbfounded," Aunty Joy told The Age.
"We would dearly love to be out there, but they've broken our hearts.
"We want to rebuild our relationship. We want to make them (realise) that this was wrong, hurtful, deceitful and tokenistic."
The Storm later released a statement blaming a "miscommunication" for the cancellation.
"There was a miscommunication of expectations regarding the use (of) Welcome to Country at Melbourne Storm events throughout the year," the club said.
"We acknowledge and accept the timing and miscommunication was not ideal and we have spoken to the groups concerned this afternoon."
Storm coach Craig Bellamy said after the game he "didn't know anything about that".
"That's the first I've heard of that," he said.
The cancellation came after several people interrupted the Welcome to Country at a Melbourne dawn service.
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