Schnebel was born in Lahr/Baden. He began general private music studies with Wilhelm Siebler from 1942 until 1945, when he started piano lessons with Wilhelm Resch, and continued study with him until 1949 at the age of 19. He continued with music history through 1952, under Eric Doflein. Simultaneously he began to study composition, from 1950, with Ernst Krenek, Theodor W. Adorno and Pierre Boulez, among others. He entered formal studies at the University of Tübingen where he took musicology with Walter Gerstenberg, as well as theology, philosophy and further piano studies. In 1955, he left with a degree in theology, but with a dissertation about Arnold Schoenberg. Soon after, he married Camilla Riegger in 1956, and the couple had a son and daughter. Schnebel became a minister, and taught theology and religion until 1963 when he began teaching philosophy and psychology. After his first wife died, he underwent a period of psychoanalysis. In 1970 he married translator Iris von Kaschnitz (1928–2014), daughter of Marie Luise Kaschnitz, and began teaching religious studies and music in Munich, which he continued until 1976. In 1976, he began teaching in Berlin as a professor of experimental music and music research, a chair created for him. He held it until his retirement in 1995.