"Two Austrian mountaineers attempted to climb the Dent-Blanche mountain" on Saturday, the police said in a statement.
"During the descent ... at 4,000 meters and for reasons which are still unknown, one of the climbers fell about 400 metres," it said.
The 27-year-old died on the spot, the police said.
In a separate incident, the police said that on Friday a 43-year-old German mountaineer failed to return after attempting to climb the 4,010 metre high Lagginhorn peak.
His body was found on Saturday at an altitude of 3,600 metres, and it appeared he had died following a 50 metre fall, the police said.
On July 15, another German climber had died from a fall on the Lagginhorn peak.