She said the Government is having a "discussion as a team" about whether there are any impacts on two-way travel.
Covid-19 Response Minister Chris Hipkins will have an update later today, Ardern said.
Auckland Airport on April 9. Last night the Ministry of Health said it was not recommending closing NZ's travel bubble with Victoria. Photo / Alex Burton
The new Melbourne case comes after Victorian officials announced on Monday that four people had tested positive to coronavirus, including a man in his 30s, a man in his 70s, a woman in her 70s and a preschool-aged child.
The group has been confirmed as having the Indian variant of the virus.
As a result a range of new restrictions will be introduced across Melbourne from 6pm tonight local time, including:
• Limiting private household gatherings to five people per day • Limiting public gatherings to 30 people • Masks will be required indoors for everyone aged 12 and over unless an exemption applies
Authorities expect the restrictions to be in place until at least June 4 but they will be reviewed throughout this period.
Multiple locations have been added to the list of sites visited by confirmed Covid cases during their infectious periods.
At a press conference this morning, Victoria's Acting Premier James Merlino said Victorians who live in Greater Melbourne will still be able to travel to regional parts of the state but must continue to follow the restrictions wherever they visit.
"For example, if you visit someone outside metropolitan Melbourne, they must have not more than five visitors at that house in that day.
"Victorians visiting regional Victoria from Melbourne will also need to wear a face mask when indoors, even when outside metropolitan Melbourne, unless an exemption applies."
Merlino said the restrictions are being brought in based on public health advice and will allow contact tracers time to "get on top" of the outbreak.
Genomic testing has found the new infections are "closely linked" to a case from a few weeks ago that originated in South Australia.
Earlier in the month a man tested positive to the virus after becoming infected while undergoing hotel quarantine in South Australia and then flying into Melbourne and returning to his home in Wollert.
Health authorities believe there could be a "missing link" between this case and the new cluster, though none of the new cases have been found to be linked to any exposure sites from the Wollert case.
'Chains of transmission' emerging
Victoria's chief health officer Professor Brett Sutton said there are "chains of transmission" playing out with the state's five new Covid-19 cases.
However, he warned there was "clearly someone who was not identified" through recent contact tracing interviews, possibly because they were a casual contact.
"That is why I flagged public transport is a risk," he said.
"I ask everyone to go back to those exposure sites on the website and, indeed, if they are going out for any gatherings, within limits from today and with 6pm restrictions in mind, go back to those exposure sites. If you have been to one of them, you should not go anywhere you should be tested."
Sutton said the fifth case in the cluster "might be the missing link" authorities have been looking for as the interview process is still ongoing.
"His initial recollections do not overlap with any of the Wollert exposure sites ... even though we know there is a genomic link," he said.
It follows the revelation that one of the cases announced yesterday was "likely quite infectious".
Sutton warned Melbourne residents on Monday "we have to ready ourselves" in case more positive cases are detected within the community.
"The viral load was high and with close contacts becoming positive, he is likely to be quite infectious," he said.
"There [was] not a huge number of close contacts but we have to go through the interview process to identify anyone else.
"We have to ready ourselves for any other positives and when there are close contacts who do become positive, that raises the possibility that even a casual contact could become positive as well."
