Firefighters say the blaze, which continued to burn into the evening, started in the refrigeration system above a cool room shortly after 6am.

Residents were initially told to close their windows and doors and turn off their airconditioners. Residents were told they could turn on their airconditioning by 4pm, although by that time the temperature in Melbourne had soared above 35 degrees.

Excavators began demolishing part of the market on Tuesday afternoon so firefighters could get inside and fight the fire internally, a Metropolitan Fire Brigade spokeswoman said.

"We will be there for some time," she said.

She said while Donald Street had been reopened to traffic, Leeds, Nicholson and Byron streets would remain closed into the evening.

It is understood the Nicholson Street premises was insured for $8 million, but according to early estimates the fire caused more than $12 million in damage.

Earlier on Tuesday, part-owner Loc Lam said he was "100 per cent" committed to rebuilding the market, which had 30 shops with 25 of them occupied.

Seafood shop owner Phat Tran was one of the first to ring triple zero when he arrived for work about 6am to find smoke coming from the building.

Workers were inside at the time, but escaped the blaze. No one was injured.

Mr Tran, speaking through an interpreter, said he had just finished renovating his decade-old shop, TNT Seafood. "He feels sad and it affects his family's income," the interpreter said.

"He doesn't know how long it will be until he has income."

His supplier Peter Simpson said the fire was devastating for the community and traders, who were preparing for a busy Christmas period.

"It's an institution, it's world-renowned and it's the hub of the Vietnamese community," Mr Simpson said.

"It's loss after loss."

The fire also destroyed at least 6000 school textbooks and Christmas presents donated to the Les Twentyman Foundation.

The foundation used most of the second level as a makeshift library for students who couldn't afford to buy their own textbooks as part of the back-to-school program, which has been running for almost 30 years.

Mr Twentyman was at the scene on Tuesday morning, watching smoke billow from the building.

"The kids are going to miss out at school next year," he said.

Jennifer Vo, who owns Saigon Rose Giftshop, said in their shop alone she thinks they have lost more than $200,000 in stock.

"I'm hurt. We've lost our income. We put so much in for Christmas – all new stock," she said.

Mr Lam, who part-owned the premises with Binh Le for more than 20 years, said he was devastated.

"A terrible thing has happened," he said.

He said the lease on the building was set to expire in April 2017 and he was planning to keep the market, but wanted to redevelop the second level.

Mr Lam said he still plans to rebuild, and keep the market.

"Yes, of course, 100 per cent," he said.

Community member Jieh-Yung Lo said the market was a symbol of the contributions made by Vietnamese migrants and multiculturalism.

"For my family, who were refugees from Vietnam, Little Saigon market was a community hub they connected with in Melbourne," he said.

"As a child, I used to go there every weekend with my parents for Asian groceries. It was the only place we could buy Vietnamese mint leaves."

Maribyrnong City Council is understood to be looking into a temporary home for the displaced traders.

Metropolitan Fire Brigade assistant chief fire officer Martin Braid said the fire started in the coolroom, most likely in refrigeration machinery, but they didn't know for certain that the fire was not suspicious .

"At this stage, we're just treating the fire as a fire," he said.