The Italian news agency ANSA said authorities had not released the names of the victims, who were skiing with two other friends when they were buried by the snowslide.
The prince was leading the group down an extremely steep, unmarked slope he had skied dozens of times when the snowslide struck, the statement said.
The accidents followed the death last weekend of a close friend of Britain's Prince Charles, who was killed in the Swiss resort of Klosters by a snowslide that narrowly missed Charles.