The principal of Melbourne's Carey Baptist Grammar School says a teacher tested positive for the coronavirus overnight, becoming Victoria's 16th case of COVID-19 and its first transmitted locally.

Key points: The teacher was tested after coming into contact with a confirmed case of coronavirus

The teacher was tested after coming into contact with a confirmed case of coronavirus Classes have been cancelled today and the school is now mapping the teacher's contacts to identify those at risk

Classes have been cancelled today and the school is now mapping the teacher's contacts to identify those at risk The Victorian Curriculum Assessment Authority has been contacted about the interruption to the senior school program

The school had yesterday announced that classes were to be cancelled today after it was discovered that the teacher, who had been in contact with someone with the virus, had shown flu-like symptoms.

A Health Department spokesperson confirmed the teacher's partner had been on the same flight from the US as Toorak GP Chris Higgins, who tested positive on Friday.

"We overnight can confirm that we have had a positive test come back on that staff member, and as a result we have one confirmed case in our school," principal Jonathan Walter said outside the school this morning.

"With that in mind, we are now going through the process of mapping the potential spread of the virus within the school with a view to then making contact with families and identifying anyone who could have been impacted."

Carey Baptist Grammar School is the first Victorian school to close due to the coronavirus outbreak. ( ABC News: Patrick Rocca )

Mr Walter said the staff member was a senior school teacher.

"I've been contact with the Education Department and also the Victorian Curriculum Assessment Authority to alert them of the interruption to our program," he said.

"We will be working carefully with them to ensure that we minimise the impact on our students here at school, particularly those in year 12 who are concerned about their results."

He said the school would make a further statement to families this afternoon.

Carey Grammar has 2,500 students including 900 in the senior school.

Mr Walter sent an email shortly before 7:30pm last night telling parents both school campuses would close on Tuesday after an adult in the school's Kew community had direct contact with a person with coronavirus and later developed symptoms.

It is the first school in Victoria to close its doors because of the outbreak.

Three more Victorian cases confirmed

Three more people were diagnosed with coronavirus yesterday, including two people who had recently travelled to the United States and one person who had returned from Iran.

Health Minister Jenny Mikakos yesterday said one of the latest cases was a man in his 50s, who was on the same flight from the US as Toorak GP Chris Higgins, who was diagnosed with the virus on Friday.

She said it was not clear whether the man had contracted the virus on the plane or afterwards.

Victorian Health Minister Jenny Mikakos announced the new cases at a press conference. ( ABC News: Ron Ekkel )

He developed mild symptoms the day after the United Airlines flight UA 0060 landed in Melbourne on February 29 about 9:30am, and is recovering at home in self-isolation.

Before his diagnosis, the man visited Wine by Sam in Seymour on March 3, between 12:30pm and 3:30pm.

On March 5, he attended a private screening of The Amber Light, a film about Scottish whisky culture, at Cinema Nova in Carlton from 7:30pm to 10:30pm.

Ms Mikakos said people who had visited those locations at those times should be aware of the symptoms of COVID-19 — but added that extended close personal contact was required for the virus to spread.

She defined close personal contact as at least 15 minutes of face-to-face time or more than two hours in the same room.

Wine by Sam owner Sam Plunkett told the ABC one of his staff members would self-isolate for 14 days after meeting the criteria of "close contact" with the man.

He said he had chosen to shut his business for a fortnight in a "particularly cautious" move which was not mandated by health authorities.

Mr Plunkett said the closure would have an impact on casual staff.

"Casual staff rely on their job for an income, and I don't believe we can find all the hours that they would have otherwise received," he said.

Woman in her 50s treated for pneumonia in hospital

The second patient from the US, a woman in her 20s, returned from Colorado on QF 94 from Los Angeles, arriving in Melbourne at 9:40am on March 6.

The third case, a woman in her 50s who returned from Tehran via Kuala Lumpur on MH 0149, arrived in Melbourne at 9:00am on March 6.

She had become unwell on February 18 while still in Tehran with a cough, fever and shortness of breath.

After she arrived in Melbourne, she was driven immediately to hospital by a relative and treated for pneumonia.

Ms Mikakos said the woman was still in quarantine in hospital in a stable condition.

Health authorities are not aware of any public exposure sites for either of the two women.

Of Victoria's confirmed COVID-19 cases, eight have recovered and six are in self-isolation, while the woman in her 50s is the only case currently being treated in hospital.

She said health authorities were not aware of any person-to-person transmission of the virus in Victoria, but expected it was "just a matter of time" until such a case emerged.

"We are very alive to the risk that we are likely to have local transmission very soon," Ms Mikakos said.

Minister rejects calls to apologise to coronavirus-infected GP

The Minister had come under pressure over the weekend for her criticism of the decision of Dr Higgins, the 11th case, to continue to work at his Toorak clinic after experiencing cold-like symptoms.

On Saturday, she said she was "flabbergasted that a doctor that has flu-like symptoms has presented to work".

Dr Higgins, who is the father of singer-songwriter Missy Higgins, said on Facebook afterwards that he felt her comments were inaccurate and unfair and requested an apology.

Chris Higgins (right), who is the father of Missy Higgins, said he had almost recovered from "mild cold" symptoms when he made the decision to return to work. ( Supplied: Instagram )

Australian Medical Association (AMA) Victoria president Julian Rait said while it was unwise for people to go to work if they were unwell, it was "unfair" to apply retrospective judgements to Dr Higgin's actions given the rapidly evolving nature of the epidemic and the advice being issued.

Calls for an apology to Dr Higgins were backed by more than 5,500 people who signed an online petition, as well as GP support group Doctors Down Under.

The not-for-profit group's Karen Price said doctors needed consistent and solid messaging and to be able to do their job without coming under attack from politicians.

"We do want her to apologise, because we need to have confidence that as this situation evolves day by day that we're not going to be left hung out high and dry," Dr Price said.

On Monday, Ms Mikakos said she valued the role doctors played in addressing the outbreak, but declined to apologise to Dr Higgins.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 2 minutes 49 seconds 2 m 49 s Ms Mikakos has shrugged off calls for her to apologise for her comments about Dr Higgins.

Instead, she said it was important that authorities operated without "fear or favour" in disclosing information about new cases, without identifying individual patients.

"I understand that this may be distressing for the individuals involved and I'm sorry if they feel distressed," she said.

"Reporting the location has happened in every single case where there has been public contact, regardless of whether the potential location of exposure is a medical practice a restaurant, a winery a cinema or an airline.

"I expect we will need to identify more workplaces and businesses as time goes on."

Screening clinics for COVID-19 have been set up at the Alfred, Eastern, Royal Melbourne, Austin and Monash hospitals, and Victorians can call 1800 675 398 for specific information and advice on the outbreak.

Government prepares for local transmission in Victoria

The state's chief health officer Brett Sutton yesterday said authorities were considering what measures might be needed once the virus began to spread within the Victorian community.

He said everyone should be staying home from work and social events if they were unwell, and workplaces should be considering remote working arrangements, supporting employee sick leave and putting in place good hygiene practises.

"We're going into a phase where that runny nose is more likely to be COVID-19 each and every day," he said.

Ms Mikakos said it was important the Government maintained its "social licence" as it considered the possibility of restrictive measures, noting Italy's decision to lock down 16 million people in the country's north.

"We have to continually evolve the advice that we're giving to the community, but having the community's support and having that social licence is absolutely critical," she said.

She stressed that state agencies were able to deliver groceries to people in self-isolation who needed it, and urged against the panic buying which has seen supermarket shelves emptied of toilet paper.

"There's no need for people to be panicking and rushing out and buying huge supplies of food or toilet paper … we will not leave people in the lurch, we will make sure that if they need that support they will get it."

The Australian Grand Prix starts in Melbourne on March 12 and could attract tens of thousands of spectators each day.

Ferrari last won the Australian Grand Prix in 2018, but is sending a smaller team this year in the wake of the coronavirus outbreak. ( AP: Asanka Brendon Ratnayake )

The race's organisers have said there will be additional precautionary measures in the wake of the COVID-19 outbreak, including more hand-washing stations and closer cleaning of facilities.

A scaled-back team of 150 will attend the race from Ferrari's northern Italian base, the last of whom are expected to arrive tomorrow.

The Bahrain Grand Prix, due to be held later this month, recently announced that fans would be banned from the track to reduce the risk of transmission.