The national airline's current Covid-19 policy states that face masks or coverings are required on all flights in all traffic light levels.
However official Government guidelines say passengers don't need to show proof of an exemption to not wear a mask on a flight, but it is highly recommended.
It has now also been confirmed that police were called to the incident on the plane.
A police spokesperson said they were called to Nelson Airport at 7.06pm on December 2 and briefly attended.
However, they said the plane had departed by the time they arrived.
E tū union head of aviation Savage said they had since been investigating the incident.
He said they understand there was a discussion by the pilot to offload the passengers on the flight, but were told by Air New Zealand they couldn't do so due to the current rules around mask exemption.
"The ability of the pilot to offload the passengers was limited because the rules clearly state a person is not required to show their exemption."
Savage said it wasn't just refusing to wear a mask that raised concerns.
"It appeared they were anti-vaccination and anti-mask wearing, they were quite belligerent and rude to people around them."
He said fellow passengers on the plane were also quite concerned.
These allegations were referred to Air New Zealand but the airline refused to comment.
When asked about the incident, New Zealand Airlines Pilots' Association President Captain Andrew Ridling said he couldn't speak to the specific case as he wasn't involved with it.
However, Ridling told the Herald pilots are ultimately responsible for making decisions onboard the plane.
"They can remove any passenger from their aircraft if the situation warrants this."
Ridling said they greatly appreciate that the vast majority of passengers follow the rules.
He said he's not personally aware of any other instances of passengers refusing to wear a mask on a flight in New Zealand.
The incident has fuelled calls from the E tū union to change the mask rules.
Savage said this would help stop unruly passengers getting on planes.
"We just want to make sure that if someone has got an exemption for wearing a mask that the cabin crew or the ground staff are not having to confront that person or get themselves into any situation where a person is going to get offended for being asked."
He said they would like to work with the airlines to help get the rules changed to better protect union members and their employees.
