But there was warning these strains would continue to show up in managed isolation facilities across New Zealand.
"We expect we will continue to see both the UK variant and South Africa variant in positive cases in our managed isolation facilities here in New Zealand as these forms of the virus become increasingly common around the world," said the ministry.
All positive Covid-19 tests are sent to ESR for whole genome sequencing as part of ongoing surveillance and our overall elimination strategy.
At January 11, there were 19 cases of the UK strain (B.1.1.7) and one case of the South Africa variant (B.1.351) in New Zealand since December 13, 2020.
Earlier last week the ministry said: "Current research suggests the B.1.1.7 variant is around one-and-a-half times more transmissible than previous variants but there is no evidence at this stage that the length of the infection period is any different to any other variant of Covid-19, nor is there evidence that it causes more severe illness. We are also closely monitoring emerging research on the B.1.351 variant."
There are currently 76 people with Covid in quarantine across New Zealand.
Yesterday's new cases
It comes as New Zealand saw six new coronavirus cases in managed isolation, including one traveller from South Africa who tested positive on day 24.
The infected travellers came from South Africa, Britain, Zimbabwe, America and Russia.
The case from South Africa was within a travel bubble of a previously confirmed case reported on December 31. The infected person has been in the Auckland quarantine facility since the contact case was detected.
Another person who travelled from the United Kingdom tested positive on day 12. They arrived in New Zealand on December 29 via the United Arab Emirates.
An international mariner also tested positive. The ministry said this person was part of an international fishing crew which left New Zealand via ship on December 18. There had been a previous history of overseas Covid-like illness in family members and a weak positive test resulted in a clinical assessment deeming it a historical case.
The seaman arrived in New Zealand from Russia and was screened for Covid around day zero as part of routine testing in transit.
One person from the United States tested positive around day three. They arrived in the country on January 14.
Another traveller who passed through the United Arab Emirates from an unnamed country tested positive around day nine and had been moved to an Auckland quarantine facility.
One person who arrived on January 9 from Zimbabwe tested positive on day nine, and a traveller who arrived from the United Kingdom on December 29 tested positive on day 12. They were both in quarantine facilities in Auckland.
This week the ministry moved to strengthen the border with day 0/1 test and pre-departure testing for all passengers with the exception of those from Australia, Antarctica and most Pacific Islands.