The avalanche happened Val Vény, a valley close to Mont Blanc near Courmayeur.
It is thought that they were part of a group of around 20, and up to four people are still missing, according to La Repubblica.
Another avalanche that hit about the same time in Colle San Carlo involved two skiers, but Walter said neither needed rescue.
Italian newspaper La Stampa reports it is likely the skiers were foreign.
Nearby skiers dug through the snow trying to uncover anyone who was missing, Corriere Della Sela reports.
The National Mountain Rescue Corps confirmed on Twitter that two helicopters have been sent to the scene of the avalanche, and the operation is ongoing.
Rescue dogs are also being used to find people caught in the tragedy.
It comes days after six mountain climbers died after slabs of ice fell on them in two separate incidents within hours of each other in the Alps.
The February 16 deaths happened in Italy and France, with a sudden rise in temperatures blamed for frozen waterfalls detaching from mountainsides.
The four climbers killed in Italy were scaling a waterfall in Gressony-Saint-Jean, in the Val d'Aosta region near the border with Switzerland, when part of the ice wall gave way at around 10.30am.
In the French Alps, two men were killed at around midday near the town of La Grave.
Julien Michon, of the mountain rescue service in Briancon, said an ice sheet broke off and crashed down on them.
Michon said the weather there was unusually warm and sunny.
- with AP
