The theft occurred when the train stopped at Geneva Cornavin station, always busy, where a number of people left and boarded the train.
In the bustle that lasted just a few seconds, Vernikov briefly lost sight of the violin case, stored just behind him on the train. He then realized it had gone.
In the case with the violin were four bows with a value of 250,000 Swiss francs.
The theft was confirmed to news agencies by Geneva police.
“It's as though someone's stolen my baby,” Vernikov told Le Matin newspaper. “Without it I can never make music again.”
The musician thinks that the thieves probably didn't know what they were stealing but just seized an opportunity. Three years ago he had his wallet stolen in the same place, he said.
Vernikov, who is from Ukraine, was appointed artistic director of the Sion Festival in 2013.
The violinist has asked anyone with information concerning the theft to contact him via his Facebook page.