The first infection was reported on Saturday in a school principal who had left mandatory quarantine weeks ago after returning a negative test result.
His case appears to be linked to a simultaneous community outbreak in New Caledonia which went into a lockdown at midnight after recording its first nine community cases.
The authorities in Wallis now report 19 cases in total, including the first on the island of Futuna.
Passenger air traffic has been suspended.
Until the weekend, both New Caledonia and Wallis and Futuna were the only French-administered territories without Covid-19 in the community.