The ministry said emerging data suggested BA.2.12.1 was 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."
The public health settings already in place to manage other Omicron variants were assessed to be appropriate for managing subvariants present in the community and no changes are required, the ministry said.
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.
However, health authorities said the presence of these subvariants in the community was 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.
The ministry said as with all variants of Omicron, the public health advice remained the same. Getting boosted remained one of the best defences against Covid.
Wear a mask indoors, stay home if you're unwell, get tested if you're symptomatic, and get vaccinated, the ministry said.
The vast majority of recently sequenced cases in New Zealand continued to be of the Omicron BA.2 sub-variant with small number of cases with the BA.1 sub-variant.
"We are continuing to monitor transmission of all variants across the country and internationally.
"These latest detections emphasise the importance of continued wastewater testing, as increasingly ESR sequencing is able to refine what its testing detects. The sequencing can determine that either BA.4 or BA.5 subvariant or both may be present but is not able to be more specific at this stage."
The people whose deaths were reported today had died in the past 10 days, apart from one death on May 6 and one death on April 11.
The total number of publicly reported deaths with Covid-19 is 1086 and the seven-day rolling average is 10.
Of the people whose deaths are reported 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.
The locations of today's community cases are: Northland (237), Auckland (2617), Waikato (602), Bay of Plenty (270), Lakes (137), Hawke's Bay (217), MidCentral (247), Whanganui (78), Taranaki (249), Tairāwhiti (46), Wairarapa (85), Capital and Coast (632), Hutt Valley (221), Nelson Marlborough (356), Canterbury (1284), South Canterbury (165), Southern (617) and the West Coast (87).
The locations of three cases is unknown.
There are 51,133 active cases of the virus in the community in total.
Meanwhile, the ministry has reported 78 new imported cases.
There are 368 cases in hospitals across Aotearoa. They are in: Northland (10), Waitematā (39), Counties Manukau (23), Auckland (61), Waikato (24), Bay of Plenty (nine), Lakes (one), Tairāwhiti (one), Hawke's Bay (19), Taranaki (nine), Whanganui (six), MidCentral (14), Wairarapa (three), Hutt Valley (nine), Capital and Coast (33), Nelson Marlborough (seven), Canterbury (50), South Canterbury (17), West Coast (one) and the Southern region (32).
The average of cases hospitalised in the Northern region (Northland and Auckland) is 59.
The seven-day rolling average of community case numbers today is 7308 while last Wednesday, it was 8024.
In the seven days to May 25, one million rapid antigen tests have been dispatched across the country.
On Covid-19 vaccinations, 95.2 per cent of eligible New Zealanders have had two doses and 70.7 per cent of those eligible are boosted.
For Māori, these figures are 88.3 per cent and 53.5 per cent, respectively.
Schools grapple with relief teacher shortage
President of the New Zealand Principal's Federation, Cherie Taylor-Patel, said during winter all schools have always had issues finding relief teachers but this year the impact of Covid was making the situation more difficult.
"Schools are having to be incredibly resourceful and they are using all the different ways they can to cover classes and to make sure that students have good days of learning but it is definitely a challenge."
Mt Roskill Grammar School has changed its daily schedule from five periods to four periods on Friday and this schedule will remain for two weeks.
The school said this system allowed for classes to be staffed effectively by those teachers who were not isolating or feeling unwell and allowed for all students to continue going to school.
School for those students starts at the normal time of 8.55am but finishes most days at 1.35pm and 1.30pm on Wednesdays.
Avondale College has also had to adapt as a significant amount of staff have become unwell.
Tomorrow, a rostering home system comes into effect which sees each year group take turns to learn from home one day a week.
"Rostering home will continue until we are confident we can advise staffing levels have returned to normal," the school wrote in a notice.
"Schools are working really hard to try and keep programmes consistent, to make sure they've got the sequential nature that sees students making progress and achieving key milestones," said Taylor-Patel.
Taylor-Patel said disruptions to teaching not only impact students learning but also their wellbeing.
She said staff shortages and no luck finding relieving teachers means other teachers have to work more, often in their release time, to cover classes and opportunities to offer specialist, support and extension teaching programmes are reduced.
"There is certainly a knock-on effect, people being unwell, it definitely impacts on the whole organisation but also on the wellbeing of students."