The flight to Sydney had to be cancelled, as well as the aircraft's flight from Sydney to Queenstown today.
An Australian woman who was on the plane told Stuff passengers were informed that a man had claimed to have a bomb.
She said initially passengers were unsure why the aircraft was being held up on the runway before being told it was due to a "security incident" and they needed to return to the gate.
"The captain came out and said the guy had said that he had a bomb on board," she said.
Passengers were kept on the plane for about an hour before police boarded and arrested a man without incident she said. Sniffer dogs were also used to check the man's seat and overhead luggage compartment, she told Stuff.
Passengers were then put up at a hotel for the night.
An Air New Zealand spokesperson said flight 711 had to be cancelled as it would no longer meet Sydney Airport's curfew requirements.
"The aircraft was also due to operate NZ832 from Sydney to Queenstown tomorrow morning and this service has also unfortunately had to be cancelled," the airline 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."