Born in Zagreb in 1914, Šulek began his music study very early by learning piano, violin, and composition. In 1936 he received his diploma from the Zagreb Academy of Music, where he studied violin with Vaclav Huml (1880–1953) and composition with Blagoje Bersa (1873–1934), the founder of Croatian modern music movements. Until 1952 Šulek was an active soloist who gave numerous recitals. He was also an active chamber music performer of the highest level, as he was the first violin of the Zagreb String Quartet from 1936 to 1938 and was a member of the Maček-Šulek-Janigro Trio from 1939 to 1945. At the Zagreb Conservatorium, Šulek began teaching violin in 1939, composition in 1948, and orchestration in 1953.
His works were played on a national and international level beginning in 1945 in Europe, South America, and the United States. Šulek became a corresponding member of the Croatian Academy of the Arts and Sciences in 1948 and an official member and secretary of the Department of Music for the academy in 1954. He launched a successful conducting career in building up an international reputation for the Chamber Orchestra of the Zagreb (now Croatian) Radio and Television. From 1958 to 1964 he was the principal conductor of both the chamber and symphony orchestras of Zagreb and undertook numerous European tours with these orchestras. He was frequently invited to be a guest conductor for the symphony orchestras of Zagreb, Belgrade, and Slovenia.
In his teaching career, Šulek was a distinguished professor of musical composition and mentor of many leading Croatian composers. his students including Milko Kelemen, Stanko Horvat, Krešimir Šipuš, Sandro Zaninović, Pavle Dešpalj, Dubravko Detoni, Igor Kuljerić etc.
