As part of the Government's child wellbeing approach, the Ministry of Education is offering $150 per pupil at decile 1-7 state and state-integrated schools over the next four years, if they do not ask parents for school donations.
The aim was to stop schools from charging school donations for class activities, which put financial pressure on parents who could not afford the money.
The scheme requires a law change and is planned to come into effect from the start of the 2020 school year.
The letter, outlining principals' concerns about the new scheme, was drafted at a recent conference of the Otago and Southland secondary principals' associations.
It was sent to Mr Hipkins earlier this week, and while the ministry had acknowledged receipt, no response had been received yet.
Otago Secondary Principals' Association president Judith Forbes declined to release a copy of the letter to the Otago Daily Times because she wanted to give the ministry time to respond.
However, she did outline some of its content.
"As principals, we are committed to the aspirational goal of free schooling for New Zealand pupils, but that isn't possible unless the state funding of schools is sufficient to meet the quality of education which we are expected to provide.
"$150 is plainly not enough for secondary schools," she said.
She personally believed a more realistic amount would be $300 per pupil.
"The letter asks the ministry to think again and consult more widely, in the hope more funding can be provided in some way."
The letter was widely supported by Otago and Southland's secondary principals.
She said principals' main concerns were that if they adopted the scheme, they would experience "huge drops" in funding, and would not be able to afford the rich curriculum experiences they are providing at present.
"Things like outdoor education, well-equipped science laboratories, digital technology, trips for geography and history."
Southland Secondary Principals' Association president Jarlath Kelly said if schools could not recover the costs of curriculum experiences, it could potentially put some teaching jobs and subjects at risk in some schools.
"That sort of pressure around [cost] recoveries may mean some subjects are unsustainable."
Mrs Forbes said principals also recognised they may alienate some families by not opting in.
"We're incredibly grateful to our parent communities for the amazing support that they have shown to schools.
"We do not want to damage the relationship that we have with our parent communities.
"We want to preserve high quality education, which we are expected to do, to prepare 21st century young people for an increasingly complex world.
"But we can't do that without adequate funding."
She said schools were still "grappling" with the decision about whether to take up the offer or not.
In early October, a Ministry of Education spokeswoman said only about a third of eligible primary and secondary schools nationwide had opted in.
However, the ministry declined to provide an update on the numbers yesterday.
"Further information, including for regions, will be available once all eligible schools have had the time to consult with their communities and consider whether the scheme is something they want to opt in to.
"Schools still have more than two weeks to make that decision."
