The boy was with a group of seven adults and six children who had spent the previous night at the Monte Rosa mountain hut at 2,883 metres, Valais cantonal police said.
They descended from the hut in the direction of Rotenboden with the intention of taking the train from Zermatt, police said in a news release.
They crossed the Gorner Glacier in two groups roped together, with eight in the first group and five in the second, police said.
At around 11.15am, a piece of rock suddenly became detached above the route and struck the boy, who was the fifth person in the first group, according to the news release.
A member of one of the groups immediately contacted emergency services, police said.
Medics transported to the site by helicopter tended to the gravely injured boy who was flown by Air Zermatt to a hospital in Bern.
He died at the hospital at 1.45pm, police said.
The prosecutor’s office for the canton of Valais has launched an investigation to determine the causes of the accident.