Passengers told to quarantine at their own cost after volunteering to give up seats on Air New Zealand flight

Two passengers who volunteered to be removed from a flight to Brisbane so that others could get back to their home countries have said they were panicked and scared after being told they'd have to pay to go into quarantine as a result.

Desiraye Solomon and daughter Delia Brown were set to depart Auckland on Air NZ flight NZ151 on Saturday after visiting a family member in New Zealand who had recently suffered a heart attack.

But the flight's payload was larger and heavier than expected, which meant some passengers had to be offloaded.

"We boarded the plane and we were waiting for a while then the captain came on and said they needed to balance the plane," Solomon said.

"So they were moving freight and luggage from one side to the other, and then the pilot came back on and said they hadn't been able to balance things and that the plane is too heavy, so they're either going to take luggage off or take passengers off.

"At that point we signaled the staff, and offered to get off the plane, we were only going to Brisbane, but other people on the plane were going to Germany."

There were also passengers returning to the United States and the United Kingdom onboard.

"We knew how stressful it was for everyone trying to get home from far away. It had been the fourth flight for one lady who was part of the group who got off the plane," she said.

Solomon said they were in a comparatively good position - they had family they could stay with and also had friends on a Tuesday flight, which Air NZ could move them on to.

But Solomon and her daughter were then asked by a Ministry of Health worker what hotel they were going to stay in - the first time they knew anything about having to go into quarantine.

The pair became confused and scared when they realised they'd have to pay for all the accommodation, food and drink charges of the quarantine - and even considered running away.

"I just thought, 'I'm gonna bolt'. We were just in panic mode," Solomon said.

Air NZ confirmed there was an issue with the weight of the aircraft and apologised for how passengers - including Solomon and Brown - were treated.

"Once our airport team realised the mistake, they re-gathered the passengers, apologised and provided our standard offload letter which lets our customers know they have been rebooked on an alternative service and that the letter may be used to claim on travel insurance if required," the airline said.

Air NZ said its been in contact with the customers affected and are in the process of arranging alternative travel, including Tuesday's flight to Brisbane.

Passengers now travelling on that flight are required by the Ministry of Health to self-isolate in Auckland before continuing their journey.