It comes as another 11 people have died with Covid-19 and another 8150 new community cases have been detected.
The subvariant was detected in the Hawke's Bay from a test returned on 10 May.
"This Omicron subvariant is prevalent in the USA and has been detected at our border for many weeks - there have been 29 imported cases reported since April, so its movement into the community is not unexpected," the ministry said.
"Emerging data suggests BA.2.12.1 is marginally more transmissible than the subvariants currently circulating in Aotearoa-New Zealand. Our genomic surveillance (genomes and wastewater) remains in place to study any new variants and track their spread.
""Meanwhile, the Omicron BA.4 and/or BA.5 subvariants have been detected in wastewater samples at Rosedale on Auckland's North Shore and in Gisborne.
"The presence of these subvariants in the community is also not unexpected.
"The BA.4 and BA.5 subvariants are being monitored by the World Health Organisation; to date, compared to BA.2, there is clinical data to suggest an increased transmissibility but no data suggesting it causes more severe illness."
There are also 368 hospitalisations including 11 in ICU.
The rolling average of community case numbers today is 7308 - last Wednesday, it was 8024.
Of deaths, the ministry said: "The deaths being reported today are for people who have died in the past 10 days, apart from one death on 6 May and one death on 11 April.
"Delays to reporting can be associated with people dying with Covid-19, rather than from Covid-19, and Covid being discovered only after they have died. These deaths take the total number of publicly reported deaths with Covid-19 to 1,086 and the seven-day rolling average of reported deaths is 10.
"Of the people whose deaths we are reporting today; two were from the Auckland region, one was from Waikato, two were from Taranaki, one was from Hawke's Bay, one was from MidCentral, three were from Canterbury, and one was from Southern.
"One person was aged under 10, one was in their 30s, one was in their 60s, one was in their 70s, three were in their 80s, and four were aged over 90. Of these people, six were female and five were male."
Yesterday the government announced New Zealand will stay in the orange traffic light setting ahead of the Omicron winter spike.
There were 15 deaths and 8435 cases of Covid-19 reported yesterday.