The victims included five Italian nationals, one of whom was 16, and an Austrian woman.
The six were among a group of 15 people who were very close to the summit of Monte Nevoso, climbing at an altitude of more than 3,300 metres (10,800 feet), when the avalanche hit in the late morning.
The others escaped unharmed, despite earlier reports several of them were injured.
The peak, whose summit stands at 3,358 metres, is also known as Schneebiger Nock.
Four helicopters were dispatched to the area but the altitude meant they were forced to fly with minimal fuel to reduce their airborne weight, hampering the operation.
Monte Nevoso lies in the Aurina valley in the South Tyrol region of northeastern Italy.
The avalanche risk in the Italian Alps this weekend was assessed to be reasonably low, just two out of five.