There is resistance on the French Pacific island of Futuna to the mobile network which was launched last month.
According to the public broadcaster, a family supported by villagers has decided to cut off the key transmitter, saying it poses a health risk.
The report also says that there are conflicting claims about whether the device has been set up on private or public land.
A family member has joined from New Caledonia to warn that the transmitter causes illnesses.
Wallis and Futuna was the last French territory to get a mobile phone service.
Its launch followed 15 years of work on the project which had been resisted as opponents feared mobile phone contact could damage local customs.