Hipkins said Delta's highly transmissible nature was making this outbreak more difficult to contain than others, raising "big questions" about the elimination strategy
Ardern has been widely praised for her management of the pandemic, with New Zealand recording just 25 deaths and less than 2,000 cases in a population of five million.
Ardern's critics have said New Zealand has fallen behind the rest of the world after promising in November that it would be first in the queue for COVID-19 vaccines.
The 56-year-old woman, who recently returned from Europe, tested positive on Saturday, 10 days after she completed her compulsory two weeks in isolation.
"But that argument doesn't wash when Singapore, who last recorded a Covid-19 death in November, has already begun vaccinating border workers," she added.
COVID-19 Response Minister Chris Hipkins said the health ministry has purchased nine large minus 80 degree Celsius freezers that can store more than 1.5 million doses of the Pfizer-BioNTech vaccine.