Sandor Feher's body was found inside the wreck and identified by his mother, who had travelled to the Italian city of Grosseto, according to Hungary's foreign ministry.
The $450 million Costa Concordia cruise ship was carrying more than 4,200 passengers and crew when it slammed into a reef Friday off the tiny Italian island of Giglio after the captain made an unauthorized manoeuvr. The death toll stands at 11.
The number of people still unaccounted for dropped to 21 after a German passenger who was listed as missing was found alive in Germany, the Grosseto prefect's office reported.
Italian rescue workers suspended operations Wednesday after the cruise ship shifted slightly on the rocks near the Tuscan coast, creating deep concerns about the safety of divers and firefighters searching for the missing.
Jozsef Balog, a pianist working with Feher on the ship, told the Blikk newspaper that Feher was wearing a lifejacket when he decided to return to his cabin to pack his violin. Feher was last seen on deck en route to the area where he was supposed to board a lifeboat.
According to Balog, Feher helped put lifejackets on several crying children before returning to his cabin.