Born in New York, Baker studied business but turned to music as a career, becoming an organist in Concord, Massachusetts. In 1874 he moved to Germany and obtained his doctorate at Leipzig in 1882. His dissertation dealt with the music of the Seneca Indians, and was the first major work published on the music of American Indians. Themes included in the work were used by Edward MacDowell in his Indian Suite. In 1891 Baker returned to the United States, where he took the post of literary editor for Schirmer Publishing in 1892. He worked there until 1926, when he retired and moved back to Germany. He died in Dresden in 1934.
Baker translated a considerable body of books and libretti into English, and wrote often in the Musical Quarterly, a Schirmer publication. In 1900, he published the first edition of Baker's Biographical Dictionary of Musicians, which was revised after his death by Nicholas Slonimsky and is still in print in its ninth edition.