The public broadcaster says a teenager brought the virus from New Caledonia where an epidemic has been declared.
The infected patient is in hospital in Kaleveleve while health authorities have launched a campaign to prevent the spread of the disease.
The patient's home is being sprayed while staffs at the clinic rely on insect repellent.
The authorities point out that the virus can only be transmitted by a mosquito.
The outbreak in Wallis and Futuna follows spikes in several Pacific countries and territories.
Photo: 123RF A teenager is said have the first case of dengue on Futuna