Sach was born in Berlin. In his youth, he studied piano, music theory and composition. However, his doctorate from Berlin University (where he was later professor of musicology) in 1904 was on the history of art, with his thesis on the sculpture of Verrocchio. He began a career as an art historian, but gradually became more and more devoted to music, eventually being appointed director of the Staatliche Instrumentensammlung, a large collection of musical instruments. He reorganised and restored much of the collection, and his career as an organologist began.
In 1913, Sachs saw the publication of his book Real-Lexicon der Musikinstrumente, probably the most comprehensive survey of musical instruments in 200 years. In 1914 he and Erich Moritz von Hornbostel published the work for which they are probably now best known in Zeitschrift für Ethnologie, a new system of musical instrument classification. It is today known as the Sachs-Hornbostel system. It has been much revised over the years, and has been the subject of some criticism, but it remains the most widely used system of classification by ethnomusicologists and organologists.
In 1933, Sachs was dismissed from his posts in Germany by the Nazi Party because he was a Jew. Sachs consequently moved to Paris, and later to the United States, where he settled in New York City. He taught at New York University from 1937 to 1953, and also worked at the New York Public Library.
He wrote books on rhythm, dance and musical instruments, with his The History of Musical Instruments (1942), a comprehensive survey of musical instruments worldwide throughout history, seen as one of the most important. Although much of it has been superseded by more recent research, it is still seen as an essential text in the field.
Sachs died in 1959 in New York City. The American Musical Instrument Society has a "Curt Sachs Award", which it gives each year to individuals for their contributions to organology.