The five were beginning their descent of the Lagginhorn peak at about 1pm when they fell several hundred metres.
"They all died at the scene of the accident," said a statement from police in the southern canton of Valais.
"The cause has not yet been established."
The alarm was raised by a sixth member of the group who had stopped short of the summit after feeling unwell.
The Lagginhorn stands 4,010 metres high in the south west of Switzerland.