"States will determine how to manage people who have already arrived in Australia from New Zealand and who may pose a risk of transmitting the Covid-19 virus", a statement from the CMO's office said.
The fresh outbreak prompted neighbouring Australia to suspend an arrangement that allowed New Zealanders to enter Australia without serving a 14-day hotel quarantine period.
"Equally, we're reaching out to our overseas counterparts that do sequence passengers who disembark and go into isolation at other destinations, so for instance in Australia to see if we can find a match there", she explained.
The snap meeting was between Australia's Chief Medical Officer Paul Kelly and the chief health officers of Victoria, NSW and Queensland.
Auckland woke up on Monday to a three-day level three lockdown ordered by Prime Minister Jacinda Ardern after three new community cases.
The new community cases make just four in the last three months - with the lockdown the first in New Zealand in six months.
Ms Ardern, who has urged Aucklanders to "stay home", said alert levels would be reviewed in 24 hours as her Government did more testing.
The "green zone" bubble between the two countries will include new restrictions from Monday, after Auckland was moved to an Alert Level Three Covid-19 lockdown.
It is not yet clear whether the lockdown will extend beyond midnight on Wednesday. Officials said the woman hadn't been going aboard the planes herself.
Health officials said a mother - who works for a company providing laundry and catering services to worldwide flights - and her daughter tested positive Saturday, before the father returned a positive sample Sunday.
Anyone who arrived in Australia from New Zealand on Sunday will be asked to undertake a mandatory 14-day quarantine, while anyone who arrived from the country earlier in the month will be contacted by health authorities.
The fatality was New Zealand's 26th Covid-related death since the start of the pandemic.
"It's a good timely reminder to everyone".
Ardern said several scenarios are being investigated.
'We're in a position at the moment where we haven't quite identified whether or not the household cases that we picked up, whether or not there are any beyond that.
"Remember, we have been here before".
"At these times we do get heightened demand, again we just reissue that plea, if you're not symptomatic, if you're not unwell and you haven't been to any places of interest, we are not asking you to come forward and be tested", Ardern says.
"If you know someone in Auckland, give them a call". Check your jurisdiction's restrictions on gathering limits.
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