Gandolfini, who won three Emmys and a Golden Globe for his portrayal of mob boss Tony Soprano on the HBO series, suffered a heart attack, celebrity website TMZ and industry daily Variety reported.
Tributes poured in from fellow actors including Susan Sarandon, who tweeted: "So sad to lose James Gandolfini. One of the sweetest, funniest, most generous actors I've ever worked with. Sending prayers to his family."
"I'm truly heartbroken to hear that James Gandolfini has passed away. He is one of my all time favorite actors. Tragic loss," Jonah Hill wrote on the microblogging site, while Steve Carrell said it was "unbelievably sad news."
Gandolfini's agents and HBO were not immediately available to confirm the reports.
TMZ said Gandolfini was in Italy for the Taormina Film Fest in Sicily, where he was expected to participate in a roundtable discussion with Italian director Gabriele Muccino this weekend.
Gandolfini had a long film and stage career before lending his heavy stature and big grin to play a depressed mafioso in The Sopranos, a celebrated series that ran from 1999 to 2007.
His breakthrough role came as a hitman in Tony Scott's 1993 True Romance, which he followed with She's So Lovely (1997), 8 mm (1999), The Mexican (2001), The Man Who Wasn't There (2001), In the Loop (2009).
He played CIA director Leon Panetta in last year's Oscar-winning Osama bin Laden manhunt movie Zero Dark Thirty, and was seen in this year's comedy The Incredible Burt Wonderstone.
He is survived by his wife, Deborah Lin, whom he married in 2008. He had a son, Michael, with his first wife, Marcy Wudarski.