Court documents allege the flight amounted to intentional non-compliance with the lockdown because he was headed to a different alert level area without an exemption.
Police declined to elaborate on the case because the matter is now before the courts.
Auckland has been quarantined from the rest of New Zealand since the coronavirus Delta outbreak was detected in August. With the onset of the new "traffic light" system last week, many lockdown restraints have been eased for those who are vaccinated, but traffic in and out of Auckland remains restricted except for those with exemptions.
Christchurch, meanwhile, has been at alert level 2 since early September.
More than 1.8 million vehicles have been stopped at checkpoints on Auckland's northern and southern boundaries, and as of last week nearly 17,000 vehicles had been turned around.
"It's important to remember that travel across an alert level boundary remains restricted and you will be turned away if you don't have the required evidence for permitted travel, as outlined on the Covid-19 website," police have previously said.