The scheme does include some staff in boarding school hostels.
Secondary Principals Association president Vaughan Couillault told Morning Report teachers should be recognised as critical workers and included in the scheme.
"I realise it's not necessarily an education decision, it's a health one, so we don't necessarily want to shoot the messenger, however it's not a good look when you're telling the providers of an essential public good - which education is - 'bad luck, you don't qualify for the rapid antigen testing scheme and just make do with whatever you can'."
Last year's extended lockdowns in Auckland, Waikato and Northland had proved how essential education providers were to the community, he said.
Keeping schools open was important, not only for students' education and wellbeing, but to ensure the economy could prosper, he added.
"There's the education and social side for students, and then when you think about education being a public good, it's a public good because not only does it serve the educational wellbeing needs of the students, economically - for the grown ups - it looks after your babies for you, so that you can head off to work, and that's got to be good for the economy."
The Principals' Federation president, Cherie Taylor-Patel, told RNZ she understood frontline workers and the health sector needed to be prioritised as critical workers, but hoped RATs would arrive in time to be useful to schools.
"We absolutely hope that the RAT testing kits will be available to schools before they absolutely need them - before schools are in crises."
Couillault also expressed concerns about the possible timing of the RATs' arrival, should schools be added to the exemption scheme.
"It appears that, with all the good intentions in the world, they may well be arriving in the middle of March; a little bit late to the party because it's middle and end of February that it looks like we're going to need them."
Te Tai Tokerau Principals' Association president Pat Newman told Morning Report one Northland school had already had to move to distanced learning because of staffing issues and the lack of access to RATs for teachers would likely shut more schools in the region.
"As far as I'm concerned, we're being left out in the cold; in Te Tai Tokerau we do not have relievers available. Just the other day we had one teacher going between rooms because we couldn't get relievers," he said.
"I don't know what happens if it's long-term, we will have to shut up and send kids home, and then all the essential workers that are out there will have to stay home to look after their kids.
"It's just not logical, but we're used to a lot of that coming out of the Ministry of Health these days.
"It's another rash ruling from the Ministry of Health and we're used to having rather insane ones coming from them."
The Ministry of Health is being approached for comment.
