Moreland City Council voted on Wednesday night to drop all references to January 26 as Australia Day out of respect for Aboriginal people.
But its stopped short of cancelling its official Australia Day citizenship ceremony.
One councillor said hosting ceremonies and events on January 26 was "grossly insensitive" to aboriginal people.
Assistant immigration minister Alex Hawke criticised Moreland's "divisive" decision.
"The Turnbull Government strongly condemns comparisons of Australia Day with the Nazi Holocaust as deeply offensive to all Australians," he said in a statement on Thursday.
