Sutermeister was born in Feuerthalen (Schaffhausen) on 12 August 1910.  After first philological studies in Basle (Music History with Karl Neff and German Literature) and a short academic stay at Paris he studied from 1932 to 1934 at the Munich Academy for Musical Arts as a pupil of Walter Courvoisier (Harmonics and Counterpoint) and Hugo Röhr (Conducting) as well as with Carl Orff.  He was for a short time opera coach at the Berne Municipal Theatre before settling at Vaux-sur-Morges, on Lake Geneva, as a freelance composer.

Operas, partly written for radio and TV, and ballets, all the stage works world-wide performed at the most important opera houses and ballet companies, and orchestral music as well as chamber and vocal music demonstrate the wide range of Sutermeister’s musical oeuvre.

In 1958 he was made president of the Swiss Association for Mechanical Copyrights "Mechanlizenz", a post he held until 1980.  From 1963 to 1975 he was in charge of a composition class at the Hannover Hochschule fuer Musik. In 1967 he was awarded the Price of the Swiss Composers Association.  Since 1977 he was a corresponding member of the Bavarian Fine Arts Academy.

Heinrich Sutermeister died in Vaux-sur-Morges (Waadt District) on 16 March 1995.