Charmian,who played Liesl Von Trapp,has passed away following a battle with dementia, reports say.
The official Twitter page for The Sound of Music confirmed the news as it paid tribute.
20th Century Fox tweeted: "She will be forever missed."
The actress was best known for playing the eldest Von Trapp daughter in the Academy Award-winning 1965 film.
Kym Karath, who played youngest Von Trapp Gretl, said: "It is with infinite sadness that I share the tragic news that the precious and exquisite Charmian Carr,beautiful Liesl , has passed away."
Ted Chapin, president of the Rogers and Hammerstein organisation, said in a statement: "It's always sad when a member of the family passes away and in the case of the 'family' of the movie 'The Sound of Music,' it's especially sad when it is the first of the group to go.
"Charmian Carr played the oldest von Trapp child, and in some ways she maintained that role in real life guiding, cheering, supporting and generally being there for the rest of her 'sisters' and 'brothers.' "
Charmian - who was 21 when she starred in the film - became known for singing one its most famous songs, 'I Am Sixteen Going On Seventeen'.
The actress's spokesman confirmed she died on Saturday in Los Angeles, of complications from a rare form of dementia.
She was a college student when she auditioned for the film, which also starred Julie Andrews and Christopher Plummer.
Carr fully embraced audiences' reverence for the musical, frequently appearing at fan events commemorating the film, including sing-a-long performances at the Hollywood Bowl.
In 2005 she said: "I tell people that they should consider sing-a-long 'Sound Of Music' like going to a therapist.
"It's just a kind of therapy. They can move around. They can dance and talk back to the screen. They can skip their appointment with the shrink that week."
Carr went on to become an interior designer in Southern California. Her clients included Michael Jackson and "Sound of Music" screenwriter Ernest Lehman.
Carr later wrote a pair of books about her experiences, Forever Liesl and Letters To Liesl.
The actress went on to star with Anthony Perkins in the Stephen Sondheim television musical Evening Primrose.
Actor and director Seth MacFarlane wrote: "So very saddened to hear of the death of Charmian Carr. She leaves behind one of the most memorable performances in movie history."
Carr was born in Chicago on Dec 27, 1942, and moved to California when she was 13.
She is survived by two children and four grandchildren.
She is also survived by the six other actors who became part of cinematic history when they were cast as the von Trapp children.
Karath, who played Gretl said in an interview last year to commemorate the film's 50th anniversary: "
"We're second family. As adults, we were deeply bonded, so our lives have really interwoven with each other."