"Forty-one people were in the train. Two were moderately injured and nine others were slightly injured," police said in a statement.
The tourist train which winds its way through Valais's snowy mountains, slammed into the van as it was driving across a crossing near the village of Moerel.
Neither the driver of the van nor the train conductor was injured in the accident, police said.
It was not the first accident involving a tourist train in the region.