The accident occurred around 10.30am at an unguarded road crossing of the narrow-gauge mountain railway, where two of the three carriages derailed, Valais cantonal police said.
"One person has been seriously hurt," a police spokesman told AFP.
The individual was flown by an Air Zermatt helicopter for treatment at the university hospital in Bern.
Police said the drivers of both the train and the van escaped injury.
A total of 41 passengers were on the train, police said.
A video of the crash scene on the Radio-Télévision Suisse website showed the van was reduced to a crumpled wreck from the impact of the collision.
Because of the disruption to the rail iine, bus service was provided for rail passengers between Fiesch and Brig, a town with connections for the Zermatt ski resort.
It was not the first accident involving a tourist train in the Alpine region.
In July 2010, a 64-year-old Japanese woman died and dozens were injured in the derailing of the Glacier Express, which runs between Zermatt and St. Moritz — a few kilometres from the site of Monday's collision.
This video from Schweizer Radio und Fernsehen (SRF) gives an aerial view of the crash site: