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.
The cancellation came after several people interrupted the Welcome to Country at a Melbourne dawn service.
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 strongly regard this as being totally tokenistic and goes completely against their journey of reconciliation and we feel very disrespected," Djirri Djirri dancers and Aunty Joy Murphy Wandin said in a statement.
"What we do isn't a performance, it's cultural ceremony and protocol. We strongly feel this action taken by Melbourne Storm was unnecessary and has caused us hurt and disbelief in what we thought was a good relationship."
Aunty Joy added that she had wanted to honour her father Sapper James Henry Wandin who fought for Australia in World War 1.
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.
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