The council says it is supporting the 40th anniversary year of Vietnamese refugee resettlement in Australia by formally acknowledging the flag for the first time.
The yellow flag with red stripes is known as the Vietnamese Co Vang flag.
The Vietnamese Co Vang flag, a yellow flag with three horizontal red stripes, is a significant part of the identity of many Vietnamese living in Australia.
For those with ties to the former South Vietnam, it symbolises what they see as their fight for democracy and freedom against communist forces led by the former North Vietnam.
The Vietnam War ended in 1975 with the defeat of South Vietnam, leading to a massive refugee crisis with comparisons to today's humanitarian crisis in Europe.
The multicultural area around Maribyrnong, in Melbourne's inner west, holds a special place in the Vietnamese community's resettlement in the years that followed.
The former Midway Hostel in the area was the first place many Vietnamese refugees were accommodated following their arrival in Australia after the war.
Maribyrnong mayor Nam Quach says he welcomes the passing of the motion to recognise the flag of what was South Vietnam.
Mr Quach says it is important in commemorating 40 years of harmonious resettlements, highlighting that, for many people, it was the start of a new life.
"The Co Vang flag ... to be clear, it's not a sovereign flag, but it's a symbol of identity, and, particularly, the identity of the Australian-Vietnamese community and their refugee experience. And for many, it symbolises not only the identity, but also their aspirations. People have left their home country in such traumatic and difficult circumstances, and their aspirations of, I guess, fleeing persecution but also those values of democracy and freedom, that's a significant essence of what the flag means to a lot of people."
Attempts to reach the embassy of Vietnam for comment were not immediately successful.
In the past, Vietnam applied pressure when the Sydney suburb of Fairfield voted to allow flying the flag.
The Maribyrnong City Council now allows flying the Co Vang flag at specific sites during times of special significance to the Australian-Vietnamese community.
The sites include the Monument of Gratitude at Jensen Reserve in suburban Footscray and public locations deemed suitable, such as Town Hall.
Lac Lanm led the push from within the Vietnamese community in Victoria, which pursued public support for the motion.
He says there was overwhelming support for approving the flag in the Maribyrnong chamber.
"In the chamber, we had a hundred per cent of counsellors say yes to the motion -- hundred per cent. Every counsellor was in favour of the motion. Not one person in the room of more than 200 people said no. And I don't think we'll get a reverse decision in the near future."
Maribyrnong mayor Nam Quach says flying the Co Vang flag is a positive step towards recognising cultural diversity.
"The essence of it is being able to demonstrate that there are so many different communities living not only in the city of Maribyrnong, but in Australia really, and I think that's a really positive message to recognise difference but also celebrate the fact that it is recognised and there is that appreciation of different cultures, different communities, living side by side as Australians, all under the one national flag of Australia."
