The pair had recently returned from London, where they had visited a dying parent, and were granted an exemption to leave their mandatory 14-day quarantine early on compassionate grounds.
They then travelled by car from Auckland to Wellington, where they tested positive for the virus.
“This case represents an unacceptable failure of the system.
"It should never have happened, and it cannot be repeated,” she said, adding a top military leader will oversee border quarantine measures.
Before the two new cases were announced Tuesday, New Zealand had gone more than three weeks without reporting any new cases and was considered virus-free.
Health officials said the women had no contact with other people on their road trip.
Ms Ardern has advocated tough border measures to prevent another outbreak and has cancelled quarantine exemptions on compassionate grounds while the case is investigated further.
She said she had appointed Air Commodore Digby Webb, the Assistant Chief of Defence, to oversee all quarantine and managed isolation facilities.
“The suspension of compassionate exemptions will continue until such time as we can guarantee a disciplined and rigorous system at the border that ministers have confidence in,” she said.
“I know this will be upsetting to some New Zealanders seeking to return home to visit dying relatives and loved ones.
“However, the risk to our collective efforts to eliminate Covid-19 are simply too great. I cannot allow the gains we have all made to be squandered by processes not being upheld.”
Coronavirus: Everything you need to know