She moved to New York City and debuted on Broadway by age 21, where she soon found success as Mary Martin's replacement in both South Pacific and The Sound of Music.

She was raised in Duvall, Washington, where she began to study singing and piano with her maternal grandmother, Cora Wright (1874–1951), a pianist, singer and music teacher.

[3] Wright also began to sing opera at the same time, including in Mozart's The Abduction from the Seraglio and The Magic Flute.

[4] Moving to in New York City, Wright began to sing on RKO-WOR Radio with its orchestra in 1947, with Sylvan Levin conducting.

She also appeared in supper clubs, including The Palmer House Hilton in Chicago, and came to the attention of Rodgers and Hammerstein,[3] who cast her as Nellie Forbush in South Pacific (1951–54), to replace Mary Martin in the role.

[3] She then performed in non-musical productions such as Mary, Mary at The National Theatre in Washington, D.C. She also continued to sing on the radio for WCBS in her own daily show for several years[3] and recorded several albums such as Censored: Martha Wright Sings Cole Porter, Irving Berlin, Rodgers and Hart, and Others (Jubilee, 1956) and Love, Honor and All That Jazz: Songs for After the Honeymoon Is Over (RCA Victor, 1960).

On television, she appeared on The Bell Telephone Hour several times and in her own 15-minute series, The Martha Wright Show, which aired in 1954 on Sunday evenings on ABC opposite Ronald W. Reagan's General Electric Theater on CBS.

In 1980, she performed The Sounds of Rodgers and Hammerstein at The King Cole Room in The St. Regis-Sheraton Hotel in New York City, followed, in 1983, by A Salute to Burton Lane and E. Y. Harburg at the 92nd Street Y.