Air NZ estimated up to 3000 customers will be impacted by cancellations today with around 6000 inconvenienced by unexpected schedule changes.
In most cases passengers are being accommodated on alternative services and the airline is working through the process of notifying customers, it said.
Further disruptions can be expected in coming days, the airline said.
Air NZ chief operations integrity and standards officer, Captain David Morgan said
Air NZ is doing all it can to minimise disruption to customers in "very challenging" circumstances.
"Our teams are working hard on solutions and we are communicating to impacted customers as quickly as we can. We appreciate their continued patience as we respond to this developing situation."
A spokesman for Jetstar said the airline had cancelled four domestic jet services today and two tomorrow as a result of the fuel shortage in Auckland.
"We're consolidating services and rebooking passengers on alternative flights the same day," he said.
The spokesman said it was too early to assess the financial impact of the pipeline failure on the cut-price airline.
He said between Sunday and Tuesday Jetstar cancelled seven return domestic jet services affecting around 1900 passengers.