Linda Marsh was born in New York City. Her father was a physician and her mother was an off-Broadway actress and producer. After attending Bennington College, she appeared in three short-lived off-Broadway productions. In 1963, despite having only two TV episodes to her credit, she was selected by Elia Kazan to play "Thomna Sinnikoglou" in America America (1963) , receiving a Golden Globe nomination for her performance. The following year (1964), she played "Ophelia" on Broadway at the Lunt-Fontanne Theatre in John Gielgud's production of Hamlet (1964), which was filmed on-stage and released as a movie. The production boasted, among others, Hamlet (1964), Hume Cronyn, Alfred Drake, and Eileen Herlie.

Subsequent to this stage role, Linda underwent operations to reduce and reshape her nose. From this point in the mid-1960s to the late-1970s, she garnered roles in popular television programs, such as The Man from U.N.C.L.E. (1964), The Wild Wild West (1965), It Takes a Thief (1968), and I Spy (1965). Outside of guest appearances, she made four feature films and three television movies.

In 1979, after her third appearance on Hawaii Five-O (1968), she was to receive no further screen or TV credits; however, she applied her talents to television production and writing. An article by Jack Gaver in the March 22, 1964 edition of the Pittsburgh Press noted that Marsh had been selected for roles from directors such as Elia Kazan and John Gielgud over many other actresses, some with more experience.