75 travellers arrived in Wallis after spending seven days in pre-departure quarantine in Noumea and returning negative tests.
After their arrival, they were in home isolation for three days after which a further test was carried out when a Futuna resident was found to have Covid-19.
The public broadcaster said the individual has been transferred to hospital.
The territory lost its only external airlink in September when New Caledonia went into lockdown over a fresh Covid-19 community outbreak.
More than half of the population has declined to be inoculated, and in June, some of the vaccines were returned.