Travellers who have been identified as contacts to cases across the Tasman will have to test negative and self-isolate for 14 days before they depart for New Zealand.
"An additional New Zealand requirement means they will need to continue to monitor their symptoms in place and will not be allowed to travel to New Zealand until 14 days after they were at the location of interest."
Hipkins said the Government was satisfied that the risk was low for resuming quarantine-free travel, based on the advice of director-general of health Dr Ashley Bloomfield.
He added that the restrictions in Western Australia were an "additional layer of assurance".
Yesterday, Western Australia Premier Mark McGowan announced the end of the lockdown in the Perth and Peel regions - but some restrictions will remain, including mask-wearing and a 20-person limit for private indoor and outdoor gatherings.
The measures will be in place until 12.01am on Saturday, May 1.
A Victorian man testing positive in Melbourne after completing 14 days of quarantine at a West Australian hotel and a pregnant woman and her 4-year-old daughter who were quarantining in the same hotel also tested positive.
Shortly after the lockdown was announced, New Zealand immediately suspended quarantine-free travel to and from Perth.
The bubble blip came just five days after quarantine-free travel between Australia and New Zealand began.
On Sunday, Hipkins said the public health risk to New Zealand was deemed to be low.
The Government had been waiting on some additional information from Western Australia, including results from additional testing, before making the final decision.
"Until then, travel between New Zealand and Western Australia will remain paused," he said.
Contact tracing for all but seven of the 664 passengers who arrived from Perth on April 19, 21 and 23 had been completed as of Sunday.
The results of the two casual contacts in New Zealand that could be potentially linked to the Western Australian cases were expected today.
Flights have been in limbo as airlines wait for an official announcement to recommence the transtasman travel bubble.
A direct Air New Zealand / Singapore Airlines flight that had been due to arrive in Auckland this morning has been delayed and is now due to arrive 5.50am on Wednesday.
It will then depart Auckland at 10.30am and return to Perth.
Perth and Peel emerged from a three-day lockdown at midnight on Monday after recording no new Covid-19 cases for 24 hours.
"We are working to be able to confirm our position as soon as possible to give those passengers certainty," Hipkins said.
