According to her son Alec Guettel, Rodgers died Thursday in her Manhattan home after a long battle with illness.
In addition to Freaky Friday, Rodgers is also well-known for writing the 1959 Broadway hit Once Upon a Mattress, a musical based on The Princess and the Pea. The original production made a star out of Carol Burnett, and Sarah Jessica Parker went on to star in the 1996 revival. Rodgers' other shows include From A to Z, Hot Spot and The Madwoman of Central Park West.
Broadway was a family legacy for Rodgers, who was the daughter of South Pacific composer Richard Rodgers. Her son Adam is also a Tony Award-winning composer for The Light in the Piazza and her late husband, Henry Guettel, was the executive director of the Theater Development Fund.
Rodgers is survived by her sister Linda Rodgers Emory and five children.