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.
Minić was famous for his knowledge of the game and great analytical ability. FIDE awarded him the International Master title in 1964. While despite being grandmaster-strength for many years, Minic could not fulfil all of the requirements for the GM title. However, Fide awarded him an Honorary Grandmaster title in 1991.
Death
Minić was found dead by friends in his Novi Sad apartment on April 9, 2005, after failing to respond to phone and intercom calls for several days. Doctors determined that he died of a heart attack approximately four days earlier.
Minić was a virtuoso of the Sicilian Defence, which he played with great skill from either side of the board. Here is a sharp tactical win over Yugoslav grandmaster Albin Planinc at the Vidmar Memorial tournament in 1973.