"The aircraft was also due to operate NZ832 from Sydney to Queenstown tomorrow morning and this service has also unfortunately had to be cancelled," they said.
"Air New Zealand apologises for the inconvenience caused to customers on both services, however, the safety and security of all passengers and our crew is naturally our first priority."
In a statement, police said they are in attendance following the threat which they report was made on the plane while it was stationary.
"Staff on the aircraft were notified of the comment by another passenger and Police were called at 8.45pm," the statement said.
Police have escorted the person who made the comment off the plane and charges are likely.