Munch made his début with the Boston Symphony Orchestra on 27 December 1946. He was its Music Director from 1949 to 1962. Munch was also Director of the Berkshire Music Festival and Berkshire Music Center (Tanglewood) from 1951 through 1962. 

He led relaxed rehearsals which orchestra members appreciated after the authoritarian Serge Koussevitzky. Among his pupils at Tanglewood was Serge Fournier. Munch also received honorary degrees from Boston College, Boston University, Brandeis University, Harvard University, and the New England Conservatory of Music.

He excelled in the modern French repertoire, especially Claude Debussy and Maurice Ravel, and was considered to be an authoritative performer of Hector Berlioz. 

However, Munch's programs also regularly featured works by composers such as Bach, Haydn, Mozart, Beethoven, Schubert, Schumann, Brahms, and Wagner. His thirteen-year tenure in Boston included 39 world premieres and 58 American first performances, and offered audiences 168 contemporary works. Fourteen of these premieres were works commissioned by the Boston Symphony and the Koussevitzky Music Foundation to celebrate the Orchestra's 75th Anniversary in 1956. (A 15th commission was never completed.)