Beavers, an invasive exotic species, were introduced to the area in 1946 to offer locals work in the fur trade.
With no natural predators, the beavers have reproduced rapidly and are a threat to the native forest, environmentalists say.
The plan is to eradicate the North American beaver completely from the archipelago, local officials say.
According to the officials, the beaver situation is "totally out of control" in Tierra del Fuego, where the rodents have destroyed an area double the size of the city of Buenos Aires.
Adrian Schiavini, who heads the National Strategy for Invasive Exotic Species, told Argentine radio that "humane traps" would be used to cull the animals "quickly and effectively".
Mr Schiavini said the species had caused huge damage to Tierra del Fuego, at the southern tip of Argentina, by building dams in its unique river system.
Biologists say that whereas some North American trees can grow back after being damaged by beavers, South American trees tend to die off after being gnawed by the rodents.
The dams they build moreover create bogs in which many native trees are unable to grow. Dams built by beavers can reach a length of 100m (328ft).
Mr Schiavini said the plan was to bring in experts in beaver hunting from North America.
"The idea is to train a group of hunters and then choose the best from this group and put them to work in seven pilot areas on Isla Grande in Tierra del Fuego."
He said he hoped that after four years, the authorities would be able to significantly step up the speed of the cull.
The authorities in the Argentine province of Tierra del Fuego are planning to cull 100,000 beavers.