Her death was announced by the estate of the musical's creators, Rodgers & Hammerstein, on Monday.
She was diagnosed with brain cancer four weeks ago and died on Christmas Eve, news site TMZ quoted her son Ryan as saying.
"She was an actress, a ballerina and loved living her life to the fullest," he told TMZ.
Born Heather Menzies in Toronto, she was 15 when the musical film was released in 1965. It went on to win 10 Oscars, including best picture.
She played the mischievous third Von Trapp child Louisa, but her later television and film appearances did not hit the same heights.
At 23, she posed nude for Playboy magazine under the headline The Tender Trapp, a decision she said horrified her Presbyterian parents, who were originally from Scotland.
She married film producer Robert Urich in 1975, but he died in 2002.
Photo caption: Heather Menzies, second right next to Julie Andrews, has died aged 68