Christchurch Airport tweeted over the weekend that its advice not to bother turning up followed a request from the band's management to make them invisible for the safety of fans.
Fans would not be kicked out, just disappointed, the airport said.
One Direction was last in New Zealand in April 2012 and fans - who are known as Directioners - crowded outside the band's Auckland hotel hoping to catch a glimpse of them.
One Direction, which is made up of Harry Styles, Niall Horan, Zayn Malik, Liam Payne and Louis Tomlinson, shot to stardom after appearing on the British version of The X Factor.
The chart-toppers are one of a number of big pop acts to perform in New Zealand over coming weeks.
Rihanna has just played three shows at Vector Arena, and Beyonce will play four sold-out shows at the same venue later this month.
Taylor Swift and Justin Bieber are also touring New Zealand.
- AAP