"When asked many times to please put it on, this lady refused with all sorts of vague answers," she said.
"Because of just this one person, we then had to return to the terminal and get security on board to remove her and then they had to go through all the on-board luggage to find hers."
Video footage supplied to Hawke's Bay Today shows cabin staff trying to negotiate with the woman, while fellow passengers grow increasingly annoyed and vent their anger at her refusal to don a mask.
The incident put the flight almost an hour behind schedule, the plane was supposed to land at Hawke's Bay Airport at 7.15pm, but didn't touch down until a few minutes after 8pm.
The Air New Zealand website states that all passengers are required to wear a face-covering in the airport and on all Air New Zealand operated flights.
Davis, 79, was travelling back to Napier with her daughter. They were two rows in front of the passenger in question and said they weren't impressed.
Air New Zealand chief operational integrity and safety officer David Morgan said they are continuing to implement government requirements and its own conditions of carriage that require passengers to wear face coverings.
"The airline will honour exemptions as per government requirements, and Air New Zealand employees have standard procedures in place to deal with customers who fail to comply with crew instructions," he said.
Morgan added that to date, customers have been "overwhelmingly supportive of the requirement to wear a face-covering on board our flights".
After the passenger was off-loaded Davis said she and her daughter were curious with how she would get to Napier.
"If she got the bus the next day, you would still have to wear a mask on that and it would be for far longer than on the plane," Davis said.
"She simply could have just worn a mask and not got a full plane load of passengers very angry. ''