Charmian, who played Liesl von Trapp, passed away following a battle with dementia, reports say.
The actress who famously sang Sixteen Going on Seventeen in the 1965 film had auditioned for the role without prior acting or singing lessons.
Writing on her experience, she said: "Rather than make me feel like an amateur or that I was ruining the scene or upsetting the star, Bob Wise took the time to help me become an actress."
Charmian left Hollywood – shortly after starring in the Sound of Music – to focus on her family and a career in interior design.
But she continued to attend many of the film's events and released a second book "Letters to Liesl" in 2001.
Her only other screen credit was the TV movie, Evening Primrose, co-starring Anthony Perkins.
She later launched Charmian Carr Design – which included pop star Michael Jackson as one of the firm's clients.
Kym Karath, who played Gretl in the film, tweeted: "It is with infinite sadness that I share the tragic news that the precious and exquisite Charmain Carr, beautiful Liesel, has passed away."
She added: "She has been like a sister throughout my life."
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