Flight NZ249 was about an hour into its journey from Wellington on Sunday when it had a problem.
Ruth Ann Herd was a passenger on board the plane and told RNZ she was having her dinner when the inflight entertainment stopped.
"And then we dropped, then we descended and it was quite a rapid descent.
"I looked out the window and I could see we were closer to the ocean than before, and then we did a big swing and turned in another direction and I thought 'oh oh, we're being diverted or something'."
Other passengers told her they heard a grinding sound from one of the engines.
"Someone thought they saw a bit of something coming away from the plane or smoke or smoke trail of some kind."
Herd said initially passengers weren't told what was happened but she said that wasn't a bad thing, it was good not to cause panic.
She said the airline put passengers up in overnight at the Pullman Hotel in Auckland.
"It was an inconvenience but I'd rather be able to tell the story about it."
Air New Zealand said the engine was shut down, and the plane landed safely in Auckland.
"As per Air New Zealand's standard operating procedures, the engine was shut down and the aircraft was diverted to Auckland where it landed safely just after 5.20pm.
"The matter will now be investigated. The safety of our customers and team is our utmost priority."
