By Agence France-Presse
"We... mourn the passing of Heather Menzies-Urich," the Rodgers and Hammerstein Organization, which holds the rights to the musical, said on its website.
"We are all lucky to have known her, and she will happily live on in that beautiful movie. We will miss her."
Menzies-Urich, then a teenager, had the role of Louisa von Trapp, one of the children of Captain von Trapp played by Canadian actor Christopher Plummer, who starred with English actress Julie Andrews.
Menzies-Urich's son, Ryan Urich, said she had been diagnosed with brain cancer and died on Christmas Eve surrounded by family, according to celebrity website TMZ, as well as Variety magazine's website.
Menzies-Urich was born in Toronto, Canada.
Her husband Robert Urich died from cancer in 2002. He was a US television star who shot to fame in the 1970s through his series "Vegas" and "Spenser: For Hire."
After his death, Menzies-Urich founded The Robert Urich Foundation to support cancer research and patient care. On the group's website, she wrote that she tried to live by her late husband's motto: "Never give up -- never, ever give up."
"The Sound of Music" opened on Broadway in 1959 and was made into a movie in 1965 with memorable hit songs including "My Favorite Things," "Edelweiss," and the title track itself.