The 49-year-old and his 46-year-old female companion left the Bivouac Dolent – a Swiss Alpine Club cabin at 2,657m – on Thursday morning to walk to the summit of Mont Dolent, which lies on the Swiss-Italian border.
The pair, who were roped up with the woman leading, were walking on the Mont Dolent glacier at an altitude of 3,250m when she lost a crampon on the ice.
She then slipped and fell, pulling the man with her into a crevasse.
Rescue service Air Glaciers despatched two helicopters to the scene, with four guides and two doctors on board.
The victims were taken to hospital in Sion where the man died on Thursday evening.
The woman suffered minor injuries.