A Melbourne charity is desperately seeking donations as panic buying limits its ability to feed hundreds of Victoria's most vulnerable people.

Key points: Another 23 Victorian cases of COVID-19 were reported overnight, taking the national tally to more than 440

Another 23 Victorian cases of COVID-19 were reported overnight, taking the national tally to more than 440 Toorak Primary School became the first Victorian public school to close after a teacher was diagnosed with the virus

Toorak Primary School became the first Victorian public school to close after a teacher was diagnosed with the virus Hundreds of National Australia Bank (NAB) workers were sent home from the Melbourne headquarters after a worker's COVID-19 diagnosis

St Vincent de Paul Society runs soup vans around Melbourne every day and is calling on the public to remember that people experiencing homelessness cannot bulk buy and store food.

Vinnies soup vans run every day of the week but operations manager Sarah Cromie said the charity was struggling to access food from supermarkets and were "in desperate need" of canned foods, pasta and rice.

"The people we serve would also really appreciate bread, cakes, long-life milk – anything like that that we can freeze. We're also fast running out of cordial, which is a very popular drink among our friends on the streets," she said.

Volunteer crews help feed people around Melbourne every day of the year. ( ABC News: Rachel Clayton )

"The foods that we would rely on for sandwich fillings are hard to find too and items such as sugar."

Ms Cromie said Vinnies' charity partners who help supply the soup vans were also running low on stock.

Vinnies is struggling to find ingredients at supermarkets to make sandwiches to feed people around the city. ( ABC News: Rachel Clayton )

The Victorian Civil and Administrative Tribunal (VCAT) has announced it will close its offices to the public from Wednesday and conduct all critical hearings by telephone.

All non-critical hearings have been adjourned until further notice.

On Tuesday afternoon, hundreds of workers were sent home from the National Australia Bank (NAB) headquarters in Melbourne after a staff member tested positive for coronavirus.

NAB chief executive Ross McEwan said in an email to staff that a colleague "on the ground floor" had tested positive for COVID-19.

Mr McEwan said all staff were being sent home and the building at 700 Bourke Street would be "pandemically cleansed".

"All colleagues from 700 Bourke should go home and continue to work from home. We plan to have 700 Bourke Street ready for colleagues to return to work later this week," the email said.

There is also a child care centre, cafes and restaurants in the building.

Mr McEwan said the bank's health department was "working through a contact tracing exercise to determine who might be at risk of contracting the virus".

"If you are not contacted by the Health Department, your risk is low," the email said.

The evacuation has come as sports events continue to be cancelled.

Australia's richest footrace, the Stawell Gift, has been cancelled in response to the coronavirus outbreak, as Victoria's official case tally rises to 94.

The annual race brings thousands of visitors to western Victoria each year and has run every year except for four since its inception in 1878.

Last year the winners of the men's and women's races received $40,000 each in prize money. ( ABC News: Patrick Rocca )

But in a statement, the Stawell Athletic Club said the three-day Easter event could not go ahead due to the ban on non-essential mass gatherings.

"The Stawell Athletic Club is working closely with the Victorian Government, Northern Grampians Shire Council and the Victorian Athletic League in what is an involving situation," the statement said.

"This includes assessing options for potentially rescheduling the 2020 Stawell Gift to a date later in the year."

The cancellation of the Easter race comes as the number of cases of COVID-19 in Victoria continues to rise.

There are now 94 cases of the virus in the state, with another 23 cases reported on Tuesday, including one at a primary school, bringing the national total to more than 440.

Toorak Primary School shut its doors after a teacher tested positive for the virus, and St Kevin's College announced it would move all classes online for the remainder of the term after a parent tested positive for COVID-19.

Premier Daniel Andrews said additional restrictions on mass gatherings would be on the agenda when the National Cabinet, comprising the Prime Minister as well as state and territory leaders, held further discussions on Tuesday evening.

He said the meeting would consider whether they need to further reduce the size of groups that could gather under new powers imposed under a state of emergency.

Mr Andrews said the chief health officer had advised that where there is a positive test and close contact then action should be taken to close that school.

He maintained it was not necessary, at this time, to close down all schools.

"I know many, many parents are anxious, they're concerned and I know to an extent it's a bit counterintuitive that schools remain open," he said.

"But the advice is closing schools now … across the board that could make a very difficult set of circumstances even worse."

Mr Andrews said he was determined to follow the best advice.

"I don't think any of us would be safer if politicians start making it up as they go," he said.

Toorak Primary School will remain closed for the next 24 hours. ( ABC News: Billy Draper )

School to remain closed for now

Toorak Primary School will remain closed for at least the next 24 hours.

Victorian Education Department deputy secretary David Howes told ABC Radio Melbourne that the closure was a precautionary measure while the Health Department assessed the risk to the school community.

He said it was "uncertain" when students would be able to return to school.

"They will be speaking to the person who was diagnosed, and they'll be doing their contact tracing to determine the risk that might have accrued to the students and staff," he said.

"Then, they will make a judgment about whether the school can reopen or not on Wednesday, Thursday, Friday or next week," he said.

The Premier rejected criticism from some parents and private schools that the direction from the Government about closures had not been clear enough.

The chief health officer has a wide range of powers to enforce the state of emergency. ( ABC News: Billy Draper )

Mr Andrews said his children and those of the chief health officer, Brett Sutton, were at school on Tuesday.

"The moment the chief health officer recommends a different path then we will change. But that's not today," he said.

A number of schools, including Carey Baptist Grammar, St Leonard's College, Ivanhoe Grammar and Ballarat Grammar, have decided to close their doors and today St Michael's Grammar School, in St Kilda, also decided to close as a "precautionary measure".

The state of emergency gives the chief health officer the power to quarantine groups of people or place areas under quarantine.

Non-essential gatherings of more than 500 people have been banned.

Victorian galleries, museums, libraries and some schools chose to close their doors after the Government announcement.

Making the right judgements to protect health

On the way into the State Parliament, Opposition Leader Michael O'Brien urged the Premier not to use COVID-19 as an excuse to cut back the hours of Parliament.

"Let's do a full day's work and not use this as an excuse to avoid scrutiny," Mr O'Brien said.

Some MPs were not attending due to health concerns, which Mr Andrews said was perfectly acceptable.

"It's quite sensible in this workplace, and in any workplace, that people make the right judgements to protect their health," he said.

Nursing homes are also taking action to protect residents who are in the high-risk category.

Visitors are being banned for two weeks from the aged care homes run by Catholic organisation VMCH from today due to health concerns.

The organisation runs 11 aged care homes across Melbourne and regional Victoria.

'Funny vibe' in the city

Some commuters said other passengers were more wary of sitting too close to other people. ( ABC News: Billy Draper )

At Southern Cross train station in Melbourne, commuters were getting used to the "vibe" of the city under the state of emergency.

"People are a bit wary. Whenever someone coughs, [others] move away," one train traveller said.

A woman who commutes from Caroline Springs said she was surprised to get a seat.

"Everything — all the shops are quiet. People are really funny, really distant," she said.

"But there was a really funny vibe coming into the city."

A woman who works in a call centre said she was not able to work from home.

She said there was "an element of beginning to panic but then there's a calm as well".

"We no longer have any cups that are provided by work. We have to bring our own cups in, our own spoons," the woman said.

"Everyone's talking about washing your hands and being careful."