The incident occurred on Monday around 2.30pm when the man was with a group of four climbers who were coming down from the southern peak of the 3,798-metre mountain, police said in a news release.
The group were not roped up because the route following a ridge to the south of the peak was not considered dangerous, according to the release.
When the group came to a “seemingly harmless snow field” a snow slide swept the victim over the edge of a cliff.
He tumbled down the southeast face of the mountain and landed in the Howäng glacier, police said.
Rescue workers from Air Zermatt retrieved the body of the man, who was already dead when they found him.
The group had earlier started the climb from the Schönbielhutte, a mountain cabin.
While an investigation into the accident continues, Valais police have arrested another German, a 64-year-old woman, on suspicion of murdering her companion, a 78-year-old German man.
The man’s body was discovered on July 22nd in an apartment in Saint Gingolph, a small town on the south bank of Lake Geneva.
The death was initially reported by the woman who said that she discovered her lifeless partner after being absent for a few days, police said in a release.
During questioning the woman later admitted to beating her partner on the head with an object (not identified ) on July 5th, police said.
The woman remains in custody while the local prosecutor’s office investigates the case.