Minić's chess career was primarily in the 1960s and 1970s. He represented Yugoslavia in many competitions, including the 1962 Varna Olympiad, where he scored 6½ out of 8 games for Yugoslavia, which finished second to the Soviet Union, and the 1970 Siegen Olympiad, where he scored 8½ out of 10 for Yugoslavia, which finished third behind the Soviet Union and Hungary. Minić also served as a second to Svetozar Gligorić and Ljubomir Ljubojević, Yugoslavia's most prominent grandmasters.