The fire erupted in the building in Villars-sur Ollon, a mountain ski resort town in the canton of Vaud, early on Wednesday morning.
Police said on Thursday that identifying the victim, from Genoa, might take some time, although reports in the Italian media say he is Lorenzo Onorato, the son of Gianni Onorato, who joined MSC in 2013 after leaving rival firm, Costa Crociere.
MSC gave its condolences to the Onorato family on Thursday.
Another 20-year-old managed to save himself by jumping from a window on the third floor of the building, landing on mattresses piled up by neighbours to break his fall.
The structure consisted of 20 apartments, some of which were occupied year-round, while others were used as holiday homes. The cause of the fire is yet to be ascertained.
The building is near the ski resort of Villars-Gryon in the Vaud Alps.