Whole genome sequencing results for two Covid-19 cases with XBB.1.5 were reported by the Institute of Environmental Science and Research (ESR) late last week.
"The detection of XBB.1.5 is not unexpected, following its recent detection in Australia and globally, and our Covid-19 response accounts for the emergence of new variants," the ministry said on Monday.
Kraken was descended from the Omicron XBB subvariant, itself a cross between two earlier strains: BA.2.75 and BA.2.10.1.
The World Health Organization said it has been detected in at least 31 other countries.
While it was difficult to establish whether this variant would become the predominant one in the community, the ministry noted the proportion of cases in the USA with this variant had been "rapidly increasing" since its detection there in October last year.
"XBB.1.5 appears to be outcompeting other XBB sub-lineages and BQ.1.1 in the USA," the ministry said.
"It remains unknown how XBB.1.5 will compete against other variants in a New Zealand context, and whether this could affect the level of Covid-19 circulating in the community in the coming months.
There was no evidence at this stage to indicate XBB.1.5 caused more severe disease compared to other variants, the ministry said.
But New Zealand had a high level of immunity due to high vaccine uptake and the recent wave of infections, the ministry said.
"Vaccines are still expected to provide protection against severe disease from XBB.1.5, particularly in those who have received boosters.
"We encourage people to get their vaccine and booster doses when they fall due."
Earlier Monday, University of Auckland associate professor Dr Siouxsie Wiles said there was concern over XBB.1.5's mutations which were "better able to infect and evade immunity from vaccines".
"Often by the time it is identified in a country, it moves."
But New Zealand had tools to reduce the impact of the new strain, Wiles said. And her advice was simple.
"I would be advising people to wear masks on public transport and planes, malls, supermarkets, wherever you are around people."
As with previous strains, Wiles said people's experiences were very different with some getting very ill and others largely unaffected.
The Ministry of Health on Monday reported 2424 new cases of Covid-19 in the community - down about 100 from Sunday and just over half the 4000 cases reported on 4 January.