Baron received his education at Brooklyn College and at the Juilliard School of Music. He began his performing career as a flautist with the New York Symphony Orchestra, the New York City Opera, and the Minneapolis Symphony Orchestra, where he served as principal flautist. He was a founder-member of the New York Woodwind Quintet, and was associated with many other fine chamber groups. In addition to performing, he had a distinguished teaching career, holding positions at Juilliard and Yale School of Music, among others. He gave many first performances, including his reconstruction of Bach's Flute Sonata in A (BWV 1032).