The accident occurred shortly before 4pm in Mürrenfluh, near Lauterbrunnen, Bern cantonal police said on Monday.
The woman was with two other men who jumped ahead of her from a point known as “the Nose” above a cliff, police said in a statement.
For unknown reasons, the woman experienced difficulties after taking off and crashed into a rock wall after her parachute opened, according to the statement.
She fell and died from her injuries, police said.
Emergency rescue workers who arrived at the scene could only proclaim her death .
The woman’s death followed the death of two wingsuit flyers in the Bernese Oberland a day earlier.
Base jumping involves diving from a high place, a cliff or a tall building, with a parachute, which is opened after a freefall.
Wingsuit flying is a similar sport involving special suits that allow practitioners to “fly” while descending before opening a parachute.
The jump is usually made from a plane or a helicopter.
Swiss media identified the wingsuit flying victims on Saturday as Ludovic Woerth, a 34-year-old Frenchman.
Woerth, known among wingsuit flyers as Videoman, was known for filming his exploits with a video camera strapped to his helmet.
He and another wingsuit veteran, New Zealand expat Dan Vicary, 33, died after crashing into a pasture in the Lütschental, near Sengg.
Vicary, who had made several hundred jumps, had been living for three year near Lauterbrunnen, where he opened a store specialized in extreme sports, 20 Minuten newspaper reported.
A third wingsuit flyer, identified by a family relative and reader of The Local as an American, was injured after jumping with the two others.
Last year, Woerth and two other adventurers flew under the Aiguille du Midi bridge, at an altitude of more than 3,800 metres, above Chamonix in the French Alps, an exploit captured on camera:
Around 20 people are killed each year while taking part in the extreme sport.
Last August, wingsuit diver Mark Sutton, a stuntman who parachuted into the London 2012 Olympics dressed as James Bond, died from crashing into a mountain ridge in the Swiss Alps after jumping from a helicopter.
More than 35 people, meanwhile, have died in the Lauterbrunnen area while base jumping.