An official says the four show mild symptoms and are isolating at home.
The government reported yesterday that seven people with Covid-19 were in hospital in Noumea, including a patient transferred from Lifou.
New Caledonia went into a two-week lockdown at midday Tuesday after three Covid-19 cases were detected in three different locations the day before.
The authorities have restated that the virus is in circulation in the community and urge the public to adhere to the restrictions.
Under the lockdown rules, anyone in public must carry a written attestation justifying their movement.
Flights and ferries have stopped operating, except for flights carrying medical staff.
Vaccinations were made mandatory last week but to date only about a third of the population has had a jab.
The latest lockdown is the third, after one last year and one in March.
New Caledonia has had just over 140 Covid-19 cases but no fatality.