The incident occurred at around 13:00 (11:00 GMT) on the 4,010m (13,155ft) Lagginhorn mountain.
"The five climbers fell several hundred metres. They all died at the scene," a local police statement said.
The hikers were descending the Lagginhorn when they fell. Police said it was not yet clear what caused the accident.
The BBC's correspondent in Geneva, Imogen Foulkes, says it appears the five were roped together.
A sixth climber who had not made the final attempt at the summit, because he felt unwell, raised the alarm immediately. Police said he had been airlifted to safety by helicopter.
Police confirmed the hikers were all foreign, but said they would not disclose their nationalities until their families had been informed.
Lagginhorn is the lowest of the 4,000-metre chain of mountains in the Alps, about 10km from the Italian border. It is regarded as one of the easier peaks to climb.
Weather conditions in the area were said to be relatively good.
Five foreign climbers have fallen to their deaths in the Valais canton in the Swiss Alps.