Mujić was born on April 25, 1933. He was a striker who started his career in Velež, where he debuted for the first team at the age of 17.
Mujić played 212 matches for Velež. In the season 1955/1956 he was the best striker of the league of Yugoslavia, scoring 21 goals.
Moreover, Mujić was the first player from BiH to wear the captain band of Yugoslavia, and he played 33 matches and scored 17 goals in the shirt of the national selection. At the Olympics in Australia in 1956 he won silver with the national team, and he also played in the national team that won the fourth place at the World Championships in Chile in 1962.
Mujić ended his career in Velež in 1968, where he later became a coach and technical manager.
Besides in Velež, Mujić played in Bordeaux (1962-1963), Dinamo (1964-1965) and the Belgium Beringen (1966).
(Source: novovrijeme.ba)