Swine flu is expected to spread in Australia with seven people returning positive tests so far - most in the past day or so.
Victorian health authorities issued the warning after closing down a Melbourne school on Thursday, after two of its pupils tested positive for swine flu.
The boys, aged nine and 10, and their older brother, 12, all returned positive results after returning from a family holiday to Disneyland in the United States.
The Melbourne family, including parents Stephanie and Jim, the three boys and a daughter will spend the next fortnight, and possibly up to three weeks, voluntarily quarantined at home.
Victorian Acting Chief Medical Officer Dr Rosemary Lester said authorities were working to identify other people who'd come in close contact with the boys as well as a Mexican tourist in Victoria who also has the virus.
"I think it's inevitable that we will have community transmission, we've seen in other countries that inevitably there is community transmission," Dr Lester told reporters on Thursday.
"At this stage all we can do is employ our best efforts to ensure that we contain the disease as long as possible."
Dr Lester said Australians had no immunity to the disease and it was potentially fatal in vulnerable people.
Melbourne's Clifton Hill Primary School, which the younger boys attended, has been closed until Sunday, and the boys' immediate classmates have been given the anti-viral drug Tamiflu as a precaution.
Health authorities have advised the 485-pupil school about cleaning common areas.
The older boy attends Thornbury High School, which the Department of Education has kept open, deciding he'd not been in close contact with students.
Mum Stephanie said she thought all her boys had developed colds after returning from the US, and said her nine-year-old son Adam had been "particularly unwell".
"They (doctors) said we better do the screening because you are just on the tail end of the period we would be worried about," she told ABC radio.
"I felt very confident the situation was under control and it was just a matter of giving information about where we'd been and who we'd been in contact with and what we'd been doing over the last week or so, since we'd been back.
"I think the 10 and 12-year-olds are quite distressed and worried about it ... but they're OK."
The school, in Melbourne's inner north, was expected to reopen on Monday, principal Geoff Warren said.
"The only reason we would not open on Monday was if it spreads, but the only opportunity for infection was on Monday (the boys' first day at school after holiday)," he told AAP.
Meanwhile, a 54-year-old Mexican woman visiting family in Melbourne also has swine flu. She has been quarantined along with her partner and son.
A Sydney woman and her child, said to be aged under five, have also tested positive after arriving in Sydney on a flight from the United States last week.
They are not considered a significant risk of spreading the virus.
The child's mother tested positive to the virus while in the US and was prescribed Tamiflu. She was not considered infectious when she returned.
The child tested positive on Wednesday, health authorities said on Thursday. The child does not attend a care centre and is not considered infectious.
At last count, the World Heath Organisation said 41 countries had officially reported 10,243 cases of swine flu, including 80 deaths.