Chief Medical Officer Professor Brendan Murphy told reporters: "The New Zealand authorities would certainly be concerned about that and they would be watching that."
He added: "We're currently working with New Zealand on what would be the conditions that we would want for that sort of a border reopening to occur."
Victoria has now had 1836 total confirmed cases, a quarter of the cases in Australia, since the Covid-19 pandemic started.
Some 210 cases in the state are known to have spread through the community, rather than by travellers.
Jenny Mikakos, the Health Minister, told the Age authorities were extremely concerned about family gatherings, which have played a key role in the surge in cases after a period of stability.
"Just because you can do something does not you mean you should do it," she said.
"Yes, you have been able to go to local shopping centres, you have been able to go to cafés, you have been able to do many things in recent weeks... but it's important to understand that in particular parts of Melbourne, we have many confirmed cases."
Daniel Andrews, Victoria's Premier, had been criticised for his cautious approach to lifting restrictions, including reopening schools, but his fears appear to have been realised with rising case numbers since the state started to ease its rules earlier this month.
The Victorian Government announced it would halt any further move that would ease restrictions on movements and gatherings.
The surge in Victoria has alarmed other states, which have had few, if any, new cases for several weeks. Queensland and Western Australia, which shut their borders in March and April, said they would look at Victoria's situation before reopening them.
Despite the surge, health officials see no need to enforce the wearing of face masks. They would have limited value as absolute numbers of transmission remain "very low", said Nick Coatsworth, Australia's deputy chief medical officer.
Avoiding hugging and kissing was "arguably far more important than, say, wearing masks", he said.
