The man jumped with a colleague from the summit of Le Pleureur, a 3,704-metre peak in the Mauvoisin region on Tuesday at around 11.45am, police said in a statement.
For an unexplained reason the victim struck a rock face on the west side of the mountain at an altitude of 3,350 metres and tumbled to his death, the statement said.
An emergency rescue team from Air Glaciers arrived on the scene but the man was already dead, police said.
The accident, the fourth of this type this month, came just three days after 35-year-old Chilean died while base jumping in the Bernese Oberland.
The man, identified in media reports as Ramón Rojas, a professional base jumper known as the “Birdman”, crashed into a rock face after jumping from a ledge in Grindelwald on Sunday.
Wingsuit flying and base jumping involves leaping from cliffs, tall buildings or aircraft with a suit designed to reduce the impact of gravity, enabling users to briefly “fly” before deploying a parachute to land.
Around 20 people a year die from the high-risk activity, which is popular in the Swiss Alps in such places as the Lauterbrunnen valley in the canton of Bern.
Meanwhile, shortly after the Russian fatality, a 28-year-old Italian parasailing enthusiast plunged 900 metres to his death near Saas Grund in another part of Valais, cantonal police said.
He failed to take off properly from the summit of the Weissmies, a 4,017-metre mountain, in the accident that occurred on Tuesday around noon, police said.
A rescue team from Air Zermatt collected the man’s body.