The canton of Graubünden authorities have launched an accident investigation, the Swiss news agency SDA reported.
The landslide, near Tiefencastel on Rhaetian Railway’s Albula line, sent three carriages off the rails on Wednesday afternoon.
Trees prevented one of the three from plunging down a ravine.
The 11 injured included two Japanese citizens and one Australian.
None has life-threatening injuries.
In a tweet, federal government spokesman André Simonazzi wished all the injured a good and speedy recovery.
The Graubünden authorities said that despite the number of injured, the accident, in mountainous terrain, could have been much more serious.
The cantonal government praised rescue workers, saying the operation to evacuate passengers and tend to the injured had been exemplary and efficient, given the difficult conditions.
Heavy rain in the region of Tiefencastel on Wednesday is thought to have triggered the landslide.
Within a 12-hour period rainfall was equal to half the normal level for the entire month of August, meteorologists said.
The Albula railway line is expected to remain closed for two days.