The federal government has confirmed it will strip citizenship powers from the council as a result of the vote, with Malcolm Turnbull describing the council's decision as “an attack on Australia Day”.
The vote taken in a suburban council chamber has reverberated across the country and sparked heated debate in the nation's capital.
“The council is using a day that should unite Australians to divide Australians,” Malcolm Turnbull said.
“I recognise Australia Day and its history is complex for many Indigenous Australians but the overwhelming majority of Australians believe the 26th of January is the day and should remain our national day,” he said.
Bill Shorten also said he did not support changing the date despite it evoking "dispossession and sorrow" for Indigenous Australians.
"Reconciliation is more about changing hearts and minds than it is about moving public holidays," he said in Question Time today.
But others have applauded the City of Yarra's decision as a mark of respect for Indigenous people who say it's not a day for celebration.
Leader of the Greens, Richard di Natale said he thought it was "a brave decision and the right decision".
"Why is it that we can't choose a day when the whole nation comes together?" he asked.
Aboriginal locals have expressed the pain they feel about a day that marks British colonisation of Australia.
"It's about taking out the party element because there is no reason for us to celebrate," said Collingwood resident Ros Sultan.
Yarra Council made history on Tuesday by becoming the first in the nation to stop holding citizenship ceremonies on Australia Day out of respect for Aboriginal and Torres Strait Islander people.
City of Yarra mayor, Amanda Stone, said the unanimous vote was made after community consultation through a series of interviews and street surveys with hundreds of residents.
But it's come under fire from some other constituents about the adequacy of that consultation.
"I would say sack the council. People didn't get a say at all," said local resident George Howard.
Scottish-born publican Roberta Logan became a citizen herself on Australia Day twenty-six years ago and said "most people aren't happy".
"I don't think it's a great idea to change the day but they could incorporate an Aboriginal thing on the same day."
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Councillor Mi-Lin Chen Yi Mei, who brought the motion forward, said it was an important move because the day was not inclusive.
"It's really an opportunity to engage with the community and to educate them on Indigenous affairs," she told the meeting.
However, the federal government confirmed on Wednesday that it had stripped the council of its right to hold citizenship ceremonies under the Australian Citizenship Act.
The PM said earlier today, "Any local council that breaches its duties under the Australian Citizenship Ceremonies Code can have its authorisation to conduct citizenship ceremonies revoked".
The council was also warned of this possibility by the Assistant Minister for Immigration and Border Protection, Alex Hawke, before the vote took place on Tuesday.
Prospective citizens will instead be sent to nearby councils that still hold ceremonies.
With AAP
