"Hospitals in Auckland are safe to visit," the ministry said.
Today's second new case arrived from France on February 4 and tested positive on day three of their stay.
The ministry said neither of today's cases were connected to the managed isolation facility at the Pullman Hotel.
From today, the ministry's updates will include a running total of historical cases.
This was because there was an increasing number of people becoming infected and recovering before travelling to New Zealand.
"Our testing may detect residual viral material in people's systems, but it's important to reiterate they are no longer considered to be infectious," said the ministry.
"We've previously stated that an increase in historical cases is not unexpected."
Since January 1, there have been 25 historical cases, out of a total of 156 cases. These historical cases have all been previously reported.
The total number of active cases in New Zealand is now 67.
Meanwhile 60 people formerly housed at the Pullman Hotel in Auckland are now self-isolating across New Zealand, as they undergo an interim measure to stem any possibility of Covid-19 spreading from the facility.
Health authorities are still in the process of working out how the highly contagious South African strain managed to spread among returnees at the Pullman in recent weeks.
Yesterday the country enjoyed a rare reprieve with the Ministry of Health reporting no new cases of Covid-19 either in the community or in managed isolation.
One person remained in North Shore Hospital after testing positive while receiving treatment for an unrelated medical issue.
The returnee, who had recently arrived in from Zambia and was waiting the results of their day 3 test, had been in managed isolation when they required treatment outside the facility.
Meanwhile the Pullman Hotel has been temporarily closed for a deep clean and extensive probe.
The final 60 guests at the Pullman Hotel completed their health checks and were released yesterday.
The returnees are now required to complete another five days of self-isolation at home and get another test before re-joining the community.
It comes as MIQ nurses fear there will be another Covid-19 community outbreak if staffing numbers aren't boosted at isolation facilities across the country.
Nurses at Managed Isolation and Quarantine facilities have revealed they feel they are "drowning" due to ongoing staffing and pay issues.
Nurses were leaving in large numbers, resulting in huge gaps in their rosters.
There were also claims things had deteriorated further when the district health boards (DHBs) took over employing staff from healthcare agency Geneva towards the end of last year.
Staff at MIQ facilities didn't receive hazard pay, making it difficult to retain employees.
New Zealand Nurses Organisation (NZNO) associate professional services manager Kate Weston said these concerns needed to be addressed urgently.
"It's distressing but unfortunately it's not surprising. Our members have been contacting us with their distress around unsafe staffing in these facilities and as NZNO, we have escalated those concerns.
