The airline would pay 1,000 New Zealand dollars ($660) for each walking billboard, a company official said.
The tattoos will promote a new system that is meant to reduce check-in waiting times.
Air New Zealand marketing manager Steve Bayliss described the campaign as "a bit of fun."
"It's a ... tattoo on the back of someone's head, so they have to have their head shaved or be bald already," he told National Radio on Wednesday. "It will be an advantage for them to be bald already."
The tattoos would fade or wash off after about two weeks, he said.
Bayliss added that he won't be part of the program since he was "doing OK" in the hair department.
Local events | Contests | Headlines at a glance