The Ministry of Health is not recommending any changes to quarantine-free travel to and from Melbourne after new community cases.
It comes after officials in Victoria confirmed four new COVID-19 cases in Melbourne on Monday.
New Zealand's Ministry of Health said on Monday it was actively monitoring the situation and remains close in contact with local health agencies.
However, it is introducing restrictions for people who have been at locations of interest which states they will not be allowed to travel to New Zealand for 14 days even with a negative COVID-19 test.
There will also be testing and isolation requirements on people who have been at locations of interest, including those who have travelled back to New Zealand in recent days.
As an additional precaution, the Ministry recommends anyone in New Zealand who has visited Melbourne since May 11 to monitor for symptoms and if they develop any they should seek advice on testing from Healthline.
The Ministry said its current assessment is that the public health risk is being appropriately managed by Victorian authorities.
Earlier on Monday, Victoria's Health Minister Martin Foley said the cases include a man who was tested positive for COVID-19 on May 23 after displaying symptoms of the virus, along with a male relative of his who was asymptomatic.
Two other close family contacts also returned positive test results. They are an adult woman and a preschool-aged child - who live in separate households.
"Our public health teams have been investigating the situation and continue to interview and test all of the individuals and their contacts," he said.
The new cases bring an end to an 86-day run of no community transmission in the state.
So far, two exposure sites have been identified, including a swim school the child attended and a shopping centre, ABC news reported.
Genome sequencing is now underway to determine if the cases are linked to anyone who stayed in an MIQ facility.