Born on March 5th, 1937 in Titograd, Yugoslavia (now Podgorica, Montenegro), he achieved the title of International Master in 1962 and International Grandmaster in 1975.
Minić had various successes in international tournaments. He won the title at Maribor (1967), tied for first place with Aleksandar Matanović in Athens (1968) and shared the title at Skopje (1969) and Vrnjačka Banja (1970).
His contribution to the game extended beyond playing; he performed duties as an arbiter, a journalist, and was once a Vice President in the Association of Chess Professionals. He was also known for his involvement in team events. Minić was a player in nine Chess Olympiads, representing Yugoslavia from 1966-1980.
Minić passed away on April 5th, 2005, in Belgrade, Serbia and Montenegro. A memorial tournament bearing his name is held each year in Podgorica.