Covid-19 Response Minister Chris Hipkins said this was "disappointing".
"These people should not be travelling, there will potentially be consequences for them, for breaking the rules."
He said he would check to see airport security was operating as it should.
"They should be being checked even before they get into the airport terminal. Previous level 4 restrictions, and I just want to check to make sure this has absolutely operating as it has previously, have had people at the door at the airport terminal checking why people are entering the terminal, before they can even get anywhere near the plane."
Last night, the Aviation Security Service said it made changes when it realised some passengers were not following the rules.
When level 4 began, security officers asked only for travel documents, such as a boarding pass or travel itinerary, when people entered airports.
But changes began on Tuesday morning.
Now, a passenger had to show their boarding pass, an eligibility document and would be asked about why they were travelling.
If they did not meet the requirements they could not enter and if they objected, the police would be called.
If the police were not available they would be "handed over" to the airport company.
The universities explained the details of each case.
A Te Herenga Waka-Victoria University of Wellington spokesperson said a resident at Te Puni Village, an accommodation hall, arrived back on Sunday after breaching the Government travel orders.
"It appears they and their family did not fully understand the government guidelines.
"The resident has returned a negative Covid-19 test and is isolating in alternative university accommodation. The resident advised that they have not been to any locations of interest published on the Ministry of Health website. Our investigations show that the resident did not have close contact with anyone at the hall."
However, they confirmed the student lived in a flat, and the university ensured their flatmates were not residing at the same address.
"All students, along with all other New Zealanders, need to obey the Government's alert level guidelines. We have been impressed with how overall students have complied with the Government's rules. We are regularly communicating with students and will advise when Government rules enable students to return south to study."
Police confirmed they had issued two infringement notices to two people who flew out of Auckland with no exemption on Monday.
