However, they could be given access to student loans, which have been off-limits for most expat Kiwis until now.
Now most New Zealand citizens are treated like domestic students in Australia and their tertiary study is subsidised.
As part of education reforms announced on Monday, these subsidies would be withdrawn and New Zealanders would become full fee-paying students.
Prime Minister Bill English's office said this morning it was seeking clarity on the changes from Australian counterparts.
The proposals will require a law change and, if passed, will come into force in January 2018.
A paper outlining the reforms said that while New Zealand citizens received subsidised study in Australia, they were unable to access student loans in Australia.
"This reform will address this anomalous situation by extending loan support to such permanent residents and New Zealand citizens and removing access to [subsidised study fees], effectively treating these students the same as domestic full fee-paying students."
Newly appointed Foreign Minister Gerry Brownlee will travel to Australia in the next week to meet his Australian counterpart Julie Bishop.
Mr Brownlee said it was important to first get an understanding from Bishop about the extent of the changes and how many Kiwis they would affect.
"We've got to know exactly what the deal is. One of the most significant changes is around the student loan facility inside Australia, which may be of great help to New Zealanders studying there."
There were currently 8000 New Zealanders studying in Australia, and 6000 of them could be captured by the change, he said.
Oz Kiwi spokesman Tim Gassin, whose organisation advocates for expats in Australia, said fees would rise by 300% to 500% if the proposals went ahead.
"At the University of Melbourne, for example, this would see the annual cost of an arts degree jump from $6349 to $24,448 and the annual cost of a medicine degree jump from $10,596 to $59,968."
Mr Gassin said the changes could also put pressure on the New Zealand education budget because many expats would return home to study.
Under a trans-Tasman deal in 2015, student loans were made available to special category visa holders who went to Australia as dependent children and had lived there for at least 10 years. Around 2600 New Zealanders became eligible for loans under the deal, which came into force in January 2016.
This group would remain eligible for what are known as HELP loans under the proposed reforms.
The education reforms come two weeks after Australia tightened its citizenship rules.
While many expat New Zealanders would be exempted from those changes, those who arrived after February 2016 will face a more difficult path to citizenship.
