Gandolfini died after suffering a massive heart attack, TMZ reported, citing sources it did not identify.
His managers said in a statement he died while on vacation in Rome.
TMZ said the actor had planned to attend the 59th Taormina Film Festival this weekend.
"We're all in shock and feeling immeasurable sadness at the loss of a beloved member of our family," HBO said in a statement. "He was special man, a great talent, but more importantly a gentle and loving person who treated everyone no matter their title or position with equal respect.
"He touched so many of us over the years with his humor, his warmth and his humility. Our hearts go out to his wife and children during this terrible time. He will be deeply missed by all of us," the statement said.
Gandolfini, who won three Emmy Awards for best actor for his portrayal of neurotic mob figure Tony Soprano, was nominated for a Tony Award for best actor in 2009 for his performance in "God of Carnage."
His film credits include "Crimson Tide," "Mr. Wonderful," "True Romance," "Get Shorty," "The Mexican," "Where the Wild Things Are," "Zero Dark Thirty," "Not Fade Away," "Killing Them Softly" and "The Incredible Burt Wonderstone." He also starred in a television production of "12 Angry Men."
Gandolfini, a native of Westwood, N.J., is survived by his wife, Deborah Lin, and their daughter, Liliana Ruth, born in October, as well as a son from a previous marriage.