"Two of these people travelled on to Queensland and the authorities there have also been advised.
"The others are all being followed up in New South Wales and are being tested.
"If I receive additional information about further arrivals, I will provide further advice."
Director-General of Health Dr Ashley Bloomfield said he could not confirm reports out of Australia that 12 people had left the Pullman Hotel - where the three community cases originated - and since travelled to Australia.
"I can't confirm that," he told Newstalk ZB's Heather du Plessis-Allan this afternoon.
"I do know that of the 354 people who we have followed up from the 9th (of January), that three of those people had subsequently travelled overseas - I do not know where to."
Speaking to Australian media, Prof Kidd said the health advice around New Zealand arrivals was now being updated, to reflect the discovery of the strain.
"On Monday, I advised that anyone who had arrived in Australia on a flight from New Zealand on or since 14 January should isolate and arrange to get tested and remain in isolation until their results are known," he said.
"I am now extending that advice: Anyone who has arrived in Australia on a flight from New Zealand on or since 9 January is asked to isolate and arrange to get a test and remain in isolation until they've received a negative test result.
"In particular, if you were in hotel quarantine or were a guest or a staff member at the Pullman Hotel in Auckland, between 9 January and 14 January, please isolate at your home, arrange to get tested for COVID-19, and follow the advice of the health authorities in your state."
Meanwhile, Australia has extended the suspension of quarantine-free travel for travellers arriving from New Zealand for at least another 72 hours, in response to new community cases of Covid 19 in Auckland and Northland.
"Based on this updated information from New Zealand, including that there have been an additional 2 cases of Covid-19 in the community in New Zealand, and all being the [more contagious] variant of concern, the HPPC has recommended that the Commonwealth extend the pause for a further 72 hours," Kidd said.
This suspension of "Green Zone" travel conditions will continue until 4PM NZDT on Sunday, 30 January.
New Zealanders were previously allowed to travel to Australia without having to go into quarantine but a virus leak from the Pullman Hotel triggered a pause on the bubble.