The climber scaled the 4,478-metre peak near Zermatt and was descending with a colleague when the accident occurred at around 4.30pm, cantonal police said.
The two climbers had made a short stop at the Solvay Hut, an emergency refuge run by the Swiss Alpine Club on a ledge at 4,003 metres.
As they resumed their descent, the Dutchman passed a rope through a hook fixed to the rock face when a piece of the rock became detached, police said in a statement.
He subsequently plunged 200 metres down the east face of the Matterhorm and was killed instantly from the fall, according to the statement.
A helicopter rescue team from Air Zermatt could only note the climber’s death.
The accident came a day after a 40-year-old man from the Czech Republic died near the summit of the Zinalrothorn, a 4,221-metre peak also in the Valais Alps.
He was one of four climbers who left the Rothornhütte on Friday morning to climb to the summit, cantonal police said.
When they were 100 metres from the summit at around 9am for a reason not immediately known the victim fell down a steep slope, said.
An investigation has also been opened into this accident.