If you have booked through a travel agent, you will need to contact them if changes are needed, or to request a refund if eligible.
Air New Zealand said those with further onward connections may also be disrupted and they would be working directly with impacted customers.
Air NZ CEO Greg Foran told Newstalk ZB's Mike Hosking the cancellations of 1.5 percent of bookings were the equivalent of or 10 domestic flights out of 500 a day or one international flight out of 65 a day.
"There are still plenty of seats you can book,' he said.
Foran said sickness and staffing had both played a part in the latest decision to cut back.
"We're running sickness at the moment about two to three times normal level and we are hiring as fast as we can.
"We've brought back about 2000 people - included in that are 1100 crew and pilots - but we can't hire any faster than that because we've got to get everyone trained up and ready to go.'
Foran said this move would provide a level of insurance into the system and more surety to customers that planes they had booked on would get off the ground.
He said based on anecdotal conversations it was a mixture of Covid and seasonal flu.
He said discussions were underway about loosening rules around working while infectious with Covid.
"We're having discussions on that at the moment I think as a lot of people would be. We're in the hands of the Ministry of Health as to what they want to do. That would assist obviously, but we're just waiting."
He said demand for flights was pre-Covid for leisure flying but below for business travel.
"Actually what we're seeing is people flying for leisure is ahead of Covid and people flying for business is behind Covid so the combination of that means that we down slightly in June but actually it's pretty strong at the moment and we're seeing more and more people getting back and wanting to travel."
In a statement, Foran said by reducing the number of flights, the airline would be able to have crew on standby to cover illness, which had not been possible lately.
This announcement would help give customers a heads up to manage their travel plans accordingly, he said.
"Looking at the disruptions our customers and staff have faced over the past five weeks, we've made some adjustments to reduce short notice cancellations in the months ahead."
Crew sickness rates had been the highest in over a decade and they were stretched to capacity, Foran said.
"We see those challenges continuing not just for crew, but for our whole operation, so are making proactive changes to address them."
More than 2000 pilots, airport staff, cabin crew, engineers had been rehired or employed, he said.
"We're also exploring options to lease a crewed widebody aircraft for the busy summer period."
Air New Zealand plans to be operating at 90 percent of pre-Covid capacity for the next six months in its domestic and international schedules.
Last month, the culmination of school holidays and winter illness caused travel disruptions across the country.