Michael Arnold Kamen was born in New York City, United States, the second of four sons. His father, Saul Kamen, was a dentist, and his mother, Helen, was a teacher. He was of Jewish heritage.

While attending The High School of Music & Art in New York City, Michael Kamen became friends with Martin Fulterman (later known as Mark Snow, who composed the theme music for The X-Files among other projects). While studying the oboe, he formed a rock-classical fusion band called New York Rock & Roll Ensemble, together with classmates Fulterman and Dorian Rudnytsky along with Clifton Nivison and Brian Corrigan of Toms River, New Jersey. The group released five albums from 1968 to 1972 (Self-Titled, Reflections, Faithful Friends, Roll Over & Freedomburger). The group performed in white tie (not tuxedos), as typically worn by classical musicians. In the middle of the concert, Fulterman and Kamen would play an oboe duet. The group backed up friend and classmate Janis Ian in a concert at Alice Tully Hall in late 1967.

After graduating from high school, Kamen attended The Juilliard School, in Manhattan, New York City.