Air New Zealand spokeswoman Tracy Sneaton said it was not yet known how many passengers had been affected.
MetService meteorologist Daniel Corbett says visibility is about 800 metres this morning and is likely to improve between 10am and midday.
"Just about sunrise, fog tends to get a bit worse and then it slowly improves as the sun melts away the layer of fog on the ground,'' he said.
Ms Sneaton said all of Air New Zealand's domestic jets were operating to schedule but regional services had been put on hold.
Ms Sneaton said a flight from Rarotonga had been diverted to Wellington, where aircraft had refuelled and would be heading back to Auckland Airport.
Passengers are being told to check arrivals and departures information on the airport website.
"Very hard to predict fog, as soon as the low visibility has lifted we will be advised,'' airport spokesman Richard Llewellyn said.