The national polytechnic, Te Pūkenga, says domestic enrolments at its 16 polytechnics have jumped 20 percent.
Meanwhile, universities' domestic student numbers are up nine percent on the same time last year, a figure equivalent to about 9000 fulltime students.
The increases mean some institutions will exceed the government funding they agreed with the Tertiary Education Commission and will have to ask for more money.
Education Minister Chris Hipkins told RNZ the government was pleased with the growth and was confident it could cope with it.
He said the government last year budgeted $334 million over four years for enrolment increases across the entire sector and $141m for general tertiary education cost increases.
However, Hipkins also indicated the government might not subsidise all enrolment increases.
"Funding is not unlimited but the TEC has told tertiary providers that it does have funding available for increased enrolments in priority areas," he said.
Te Pūkenga would not provide details about its enrolments, referring RNZ to individual institutions.
Two of the largest, Unitec and Manukau Institute of Technology in Auckland, would not provide total enrolment figures, but said new enrolments were a lot higher than last year.
The institutes' deputy chief executive, Peseta Sam Lotu-Iiga, said the number of new domestic students was up 38 percent at Manukau and 22 percent at Unitec compared to the same time last year.
"Certainly it's the biggest growth in domestic numbers, probably for over seven, eight years, so it's significant growth," he said.
The director of Universities New Zealand, Chris Whelan, said domestic enrolments at the eight universities were up nine percent, which is equivalent to about 9000 fulltime students.
However, he said the universities had also lost about 14,000 foreign students, so the net result was that they were worse off by 5000 students.
"The net effect is a loss of about $150 million for the sector, or $150 million the sector is going to have to find through other efficiencies," he said.
Whelan said the universities' domestic growth was within the government's budget so he was confident it would be funded.
"The Tertiary Education Commission has been funded last year for up to a 10 percent increase so the government made a good call last year. They looked at previous recessions or downturns, they estimated there would probably be about a 10 percent increase this year so the nine percent for the university sector has come in almost exactly right," he said.
Some increases in private sector also
The picture in the private sector was more mixed.
The director of Independent Tertiary Education New Zealand, Wayne Dyer, said less than half the organisation's members were expecting more New Zealand students this year.
"Round about 45 percent expect numbers to stay the same and about 40 percent expect them to increase," he said.
Dyer said those who were expecting an increase were forecasting a median increase of about 20 percent.
He said about 15 percent of private providers were expecting their domestic enrolments would fall.
Dyer said private tertiary institutions were trying to find out from the Tertiary Education Commission how to claim funding for enrolments that exceeded the totals agreed for this year.