WELLINGTON, Jan 31 - Party leader Andrew Little announced the policy on Sunday, saying it would be phased in from 2019 and would cover university courses and other skills training.
Labour has costed it at $1.2 billion a year when fully implemented in 2025.
Tertiary Education Minister Steven Joyce says it would be likely to cost a lot more than that with no gains for the country.
"The key thing is that it would achieve nothing for tertiary education," he told NZ Newswire.
"If anything it would make it go backwards because as soon as it's free you go back to the bad old days of short courses, very low rates of achievement and spiralling costs."
Joyce says the policy is about taking more than a billion dollars a year off one group of people, taxpayers, giving it to a smaller group of people and achieving nothing except going back to the days of bums on seats.
"Fundamentally it comes down to whether anyone should make a contribution to their study, and whether it's fair to do so," he said.
"We would argue that a contribution of about 30 per cent of the value of courses is important to make - people who achieve a degree earn about 50 per cent more a year on average than those who don't."
Joyce thinks Labour hasn't considered the increase in student numbers that would result from its policy.
"More people will sign up, sure, but it's free and they don't have to achieve anything."
ACT Leader David Seymour says Labour just wants to be popular.
"Labour's approach to education is funding for votes, and quality be damned," he said.
"Moreover, students will have no skin in the game.
"Right now the deal is you back yourself, borrow a quarter of your course cost and the taxpayer picks up the remaining three-quarters.
"With Labour, everybody will have a certificate, it just might not be a very good one."