Flights by Air Caledonie from Noumea to Mare, Lifou and Ouvea have been suspended until further notice.
The pass can be obtained once seven days have elapsed after the second jab of an mRNA vaccine and 28 days after getting other vaccines.
It is also available for those who have had a fresh negative test or proof of having recovered from Covid-19.
The provisions are resisted by several groups, including unions, which also reject the new local law, making vaccinations compulsory by the end of the year.
The chiefs say they are not against vaccination but want everybody to be treated the same way.
The health service demanded the use of such a pass to limit the spread of Covid-19 which has infected about 10,000 people since the start of the latest community outbreak in early September.
Over the weekend, the government had reimposed a strict lockdown and curfew, forcing restaurants and shops to remain closed again, in a renewed effort to fight a resurgence of the virus.