Equipped with crampons, the man was descending from the 3,727-metre peak on the Italian border with a colleague, Valais cantonal police said in a news release.
When he reached the centre of the Hannibal couloir he slipped and rolled 300 metres down a slope, police said.
His colleague reached him and attempted to give first aid.
When rescue workers arrived the victim was dead, police said.
Glacier-covered Mont Vélan is located south of Bourg-Saint-Pierre in the canton of Valais and north of Etroubles in Italy’s Aosta Valley.
In another fatal accident over the weekend, a 28-year-old Swiss wingsuit flyer died in the Bernese Oberland.
The victim was with four other wingsuit enthusiasts who leaped from Oltschiburg, a 2,234-metre mountain overlooking Lake Brienz on Saturday evening, Bern cantonal police said.
According the initial findings, the man slammed into trees before falling into a ravine at around 6.30pm.
Rescue officials arrived on the scene only to find him dead, police said.
An investigation has been launched to determine the exact causes of the accident, the latest in a series of deadly incidents involving wingsuit flyers.
The extreme sport of wingsuit “flying” involves jumping from peaks ,and sometimes from helicopters or planes, wearing specially jumpsuits that allow users, equipped with parachutes, to briefly glide while in freefall.
Several people have died wingsuit flying in Switzerland over the past year, including Mark Sutton, the British stuntman who parachuted into the 2012 Summer Olympics ceremony as a James Bond character.
Sutton died after hitting a mountain ridge near Martigny after leaping out a helicopter on August 14th 2013.
Three experienced wingsuit flyers died on March 29th in the Lütschental Alps, near Bern.