Minghella died from complications following surgery last week for cancer of the tonsils and neck, agent Leslee Dart said.
“The surgery had gone well and they were very optimistic,” she said. “But he developed a haemorrhage last night and they were not able to stop it.”
He was married to Carolyn Choa and had two grown-up children, Max and Hannah. Film producer David Puttnam said it was a “shattering blow”.
“He was a great guy, a very, very nice man, a brilliant writer, excellent director and someone who contributed more than most to our industry,” Puttnam told BBC News 24 television.
“He’s going to be hugely missed.”
British Film Institute Director Amanda Nevill said: “We are deeply, deeply shocked and terribly sad. All our thoughts go out to his family.
“His art was about communicating to you and allowing you to see the world differently. He was just such a wonderful man.”
Minghella won the Academy Award for best director in 1996 for the wartime romance starring Ralph Fiennes. He was also nominated for an Oscar for his screenplay for the thriller “The Talented Mr Ripley”.
He wrote the “Cold Mountain” screenplay.“The English Patient”, based on author Michael Ondaatje’s novel, was an unexpected global hit.—Reuters