The ministry's deputy secretary sector enablement and support, Katrina Casey, said they are confident NBHS is doing "everything it can" to make sure students and staff are safe.
"Ministry of Health guidelines make it clear that in some environments like school sites it's not always practical to have physical distance restrictions in place," she said.
"Unlike public spaces, school sites are controlled environments meaning schools know who is there and who they have been in close contact with so contact tracing can take place if required."
Bertram added that maintaining the health and safety of all students and staff members is "of paramount importance" to the school.
"We are very conscious of keeping the students and staff safe, but we also want them to get back into the daily school routine.
"We are quite confident that we can do both."
The school headmaster said the school had put necessary social distancing and hygiene standards in place for all boys to follow.
Casey added that schools have also been advised to prohibit touching, including hongi, handshakes and hugs.
"We know that school leaders are focused on the safety and wellbeing of students and staff and we are supporting them with that," she said.
Earlier this week, Bertram said 94 per cent of students were at school, which was just below average for a Monday in winter.
The school's boarding hostel is also up and running and all students were present except for a few who were absent for non-Covid reasons, he said.