Jetstar said after landing the aircraft experienced a steering issue, causing it to veer on the runway at a low speed.
Freelance Journalist Diana Clement was a passenger on flight JQ225 and says it was a frightening landing.
"We swerved off the runway onto the grass then swerved violently back onto the runway before coming to a halt across the main runway."
Clement told Morning Report they were told there had been a hydraulic leak on the right hand side.
"Everyone's feeling a bit shaky."
She thought the flight itself did not feel out of the ordinary.
But she said some other passengers heard a weird noise when they were flying over, roughly New Plymouth. And then a similar noise on landing.
Andi Burrell said he heard something that "didn't sound right" during the flight.
"Probably half an hour in there was some mechanical noise coming from the right hand side of the plane," he said.
"I said to my partner at the time 'that doesn't sound right' but didn't think anything of it until we came into land."
Burrell said he felt the plane was "coming in too fast" upon landing.
"When they applied the hydraulic brakes, it failed, a bit of brake lock and it went in a jerky motion," he said.
"But at the same time it was under control but there was a bit of forward momentum.
"There was some uneasiness (on board) but the pilot was pretty good."
Another passenger, Karin Small, told RNZ she had no idea anything was wrong until the landing.
"I've never been on a plane that that's happened to before," she said.
"It skidded out and then took off again and then landed on the grass and then the fire people came.
"I was pretty calm about it and the staff were pretty good about people keeping it together."
A mother aboard the flight, Joamn Materone, said she wasn't focusing on what was happening in the cabin, rather her daughter who was upset.
"My baby was crying the whole time so I was playing with her. She was really frightened, the moment the aircraft was shaking.
"So hard - That was when I realised something was wrong.
"I'm happy that we're safe."
Materone said there was nothing during the flight which made her feel something was wrong.
"Waiting (to be disembarked) was hard.
"We were so hungry, especially my baby she was complaining about her tummy."
The Jetstar aircraft was towed to the gate for passengers to disembark.
In a statement, the Civil Aviation Authority said it was looking into the event.
"JetStar operates under the Australian Civil Aviation Safety Authority, which has also been notified," he said.
The incident happened at 7:45am on Friday.
There were no reports of injuries.
Several domestic arrivals and departures to Christchurch had to be cancelled.
