Five rescue helicopters were sent to the scene, 2,900m (9.500ft) above sea level in the Zillertal Alps.
The climbers were roped together when one of them slipped, pulling the rest of the group with him, police said.
They fell 200m (650ft) down a slope before landing in a crevasse. Only one survived, and was flown to hospital in Salzburg, about 80km (50 miles) away.
Officials say the climbers were below the Mannlkarscharte pass near Krimml, in an area where a heightened risk of rockslides made recovery of the bodies more difficult.