Ms Menzies-Urich, who also had major roles in TV series like Logan’s Run and The Six Million Dollar Man, died on Christmas Eve.
As Louisa Von Trapp, she played the third oldest of the Von Trapp children, whose escape with her family from Nazi-occupied Austria was dramatised by Richard Rodgers and Oscar Hammerstein in the 1959 musical and subsequent 1965 film.
The child actors and actresses who played the seven Von Trapp siblings became world famous for their roles and renditions of such tunes as Do-Re-Mi and So Long, Farewell.
Her son Ryan told US news site TMZ she was diagnosed with brain cancer around four weeks ago and died surrounded by her family.
“She was an actress, a ballerina and loved living her life to the fullest,” he said.
Ted Chaplin, of the Rodgers and Hammerstein agency, said: “Heather was part of ‘the family.’
“There is really no other way to describe the members of the cast of the movie of The Sound of Music.
“And of ‘the kids,’ Heather was a cheerful and positive member of the group, always hoping for the next gathering.
“We are all lucky to have known her, and she will happily live on in that beautiful movie. We will miss her.”
Born in Toronto, Canada, she was just 16 at the release of The Sound of Music, which featured Julie Andrews and Christopher Plummer in the lead roles and has become a staple of Christmas TV schedules over the years.
She was married to the actor Robert Urich, with whom she appeared in the TV series Vega$, who died of a rare form of cancer in 2002.
Mrs Menzies-Urich spent many of her subsequent years establishing and then fund raising for the Robert Urich Foundation which carried out research into treatment for cancer and provided support for patients.