The man was jumping with two others when the accident occurred on Saturday in Grindelwald, Bern cantonal police said in a statement.
He jumped from a ledge below the Glecksteinhütte, a mountain hut at an altitude of 2,317 metres southwest of the Wetterhorn, at around 11.30am but appeared to have deployed his parachute too late and crashed into a rock face, the statement indicated.
Rega emergency rescue workers were immediately alerted but the man was dead when the team arrived, police said.
In an online report, the Blick newspaper identified the victim as Ramón Rojas, a professional base jumper known as "the Birdman".
Rojas, who set a record by jumping from a 4,100-metre mountain in the Andes a month ago, abandoned a dentist degree programme to pursue the sport full time, the Zurich-based newspaper said.
The accident is yet another in a series of fatalities in Switzerland involving base jumpers or wingsuit flyers.
Both are high-risk sports involving jumps from high places, such as mountain cliffs or aircraft, by individuals equipped with parachutes who initially make a free fall before deploying the chutes.
Bern cantonal police, meanwhile, were seeking witness over another fatality — this time from a head-on collision on Sunday between two cars in Ochlenberg, a rural village in the north part of the canton.
A 68-year-old man from the canton of Bern, a driver of one of the vehicles, died at the scene of the crash despite several attempts to revive him, police said.
The 25-year-old man driving the other car was transported by ambulance to hospital for treatment.
A passenger in this vehicle, a 23-year-old woman, was taken by helicopter to hospital with serious injuries, police said.
Police believe liquids on the road, identified as the Lindenstrasse, may have played a role in the crash, which occurred shortly before 4pm.
Investigators were seeking witnesses who may have information about the condition of the road earlier in the afternoon.
Check the YouTube video below: Ramón Rojas was sponsored to do base jumps by companies such as sports brand Adidas: