Milan Vukić (born 19 August 1942, Sanski Most) is a Bosnian chess Grandmaster. He has been a champion of Bosnia and Herzegovina and of the former state of Yugoslavia, both during its constitution as a Socialist Federal Republic (SFRY) and as a Federal Republic (FRY).
Vukic only started to play chess as a young man, having been occupied with other sports during his teenage years. Once hooked on the game, his progress was rapid.
Earning the title International Master in 1967 and Grandmaster in 1975, he first won the Yugoslav Chess Championship (SFRY) in 1970 and added further victories in 1971 and 1974.
In the midst of the Balkan war hostilities (1992–1995), it was not uncommon for passionate chess players, like Vukić, to ignore the dangers and carry on playing in scheduled competitions. A fourth (this time FRY) championship win came his way in 1994. Later, after his country had endured yet more political upheaval, he won the first ever Championship of Bosnia and Herzegovina (2005). Organisers ensured this tournament comprised a mix of Serbian and Bosnian players in the spirit of friendship. Vukić was himself a registered Serbian player at the time, but has since switched Federations.
A regular on the international tournament circuit of the 1970s, he enjoyed considerable success. Notably, there were outright or shared first places at the Biel Open 1972 and 1973 (the latter shared with Janos Flesch), at the inaugural Banja Luka tournament 1974 (ahead of Vlastimil Hort and Gennady Kuzmin, other notable players included Jan Timman, Borislav Ivkov, István Csom, James Tarjan - maybe his biggest success), and at Bajmok, Varna (both 1975), Vukovar 1976 and Zemun 1980 (shared with Dragoljub Velimirović).