Health Minister Martin Foley said the border would stay closed for the next week.

"It's certainly not going to be this week and we'll continue to take the advice of public health officials as to when that (reopening) will be the case," he said.

"There is no chance of the borders reopening for New Year's Eve ... we want to make sure those borders, particularly to the red zones of Sydney and the Central Coast, stay shut down."

Mr Foley would not say when he thought those borders might reopen.

Victoria has two new coronavirus cases among returned travellers in hotel quarantine.

The infection of a woman in her 20s and a child aged 10 takes the number of active cases in the state to 11.

But Victoria is also nearing a two-month milestone for no cases of community transmission, after marking its 59-day streak on Monday.

Of the 11 active cases, 10 are in hotel quarantine.

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The other is a teenage Melbourne girl who continues to isolate at home after contracting the virus while visiting an infection hotspot in NSW earlier this month.

Victoria conducted 5880 COVID-19 tests since Sunday and wastewater monitoring continues at more than 60 sites across the state.

"There has been an excellent response to our call for testing over the past week with higher than expected numbers of people getting tested in lead up to Christmas," said Chief Health Officer Brett Sutton.

"But we must remain vigilant over the festive season and anyone with symptoms is urged to get tested immediately."

Meanwhile, Mr Foley said a man arrested and facing fines for leaving quarantine in Melbourne on the weekend "unequivocally" should have been in a hotel.

The man said he tried to leave because of his growing anxiety while in quarantine and what he claimed were mixed messages from hotel staff.

"I understand what the gentleman asserts and the facts of the matter, as they're available to me, clearly indicate this gentleman was a resident of the Sydney red zones and unequivocally was required to spend 14 days in hotel quarantine," he said.

"In this case the system worked, the gentleman was properly advised, and he was ill-advised to try to leave hotel quarantine.

"He now faces the prospect of significant fines and I would urge everybody to stay safe, to follow the rules, particularly if you are required to do hotel quarantine."

Australian Associated Press