A Melbourne council has made history 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.

Yarra City councillors voted on Tuesday night voted to stop referring to January 26 as Australia Day and to cease holding any citizenship ceremonies on that day from 2018.

Despite pressure from the federal government against such a move, all councillors voted unanimously.

All clauses passed unamended despite some fiery submissions from a few people in the audience who said the council hadn't surveyed the community widely enough.

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.

Councillors said January 26 was the wrong day for a celebration and a party.

The council's move has outraged Assistant Minister for Immigration and Border Protection Alex Hawke, who has fired off a letter to councils across the country warning they could be banned from hosting any more citizenship ceremonies if they stop holding them on Australia Day.

"Local councils are now on notice that if they politicise Australian citizenship, the government will see it as a breach of the (Australian Citizenship Ceremonies) code and take the appropriate action," he said.

Mayor Amanda Stone said she can't find any requirement in the code for councils to hold citizenship ceremonies on Australia Day.

"The code actually says you shouldn't use a ceremony to promote a political agenda or a religious agenda or commercial agenda," she told AAP.

"We wouldn't be intending to do that. We are simply considering changing when we hold our first citizenship ceremony of the year."

Yarra City usually holds citizenship ceremonies every two months.

Ms Stone said councillors took into consideration the ministers' warning before tonight's vote, but all decided a bold move for change was required.