The man slipped while climbing at 2,890 meters and fell from about 70 meters onto rocky terrain. Police said he died very quickly from his severe injuries.
The 60-year-old had been part of a five-member group of German climbers who were crossing to High Villerspitze across the Great Horntaljoch.
When the group could not overcome a rocky passage, they turned around and headed back in the direction of the Horntaljoch.
The German slipped on a ledge and plunged into the depths. His body was recovered by a police helicopter, and taken down to the valley.