Carr was born Charmian Farnon in Chicago, Illinois, the second child of vaudeville actress Rita Oehman and musician Brian Farnon.She has two sisters, both actresses (Shannon Farnon and Darleen Carr).
While Charmian was attending college part-time and working for a doctor, her mother arranged for her to audition for a role in The Sound of Music. Rita Farnon hadn't asked Charmian if she wanted to audition for the part, but Charmian was sure her mother would consider getting a part in a film more important than earning a college diploma. Director Robert Wise thought Farnon was too long a surname paired with Charmian. After he had given her a list of single syllable surnames, she chose Carr. She won the role of Liesl over Geraldine Chaplin, Patty Duke, Mia Farrow, Lesley Ann Warren and Sharon Tate