Minja was a member of the Yugoslavia national team that participated at the 1955 FIBA European Championship in Budapest, Hungary. Over nine tournament games, he averaged 6.5 points per game. At the 1957 FIBA European Championship in Sofia, Bulgaria, he averaged 10.9 points per game over nine tournament games. At the 1959 FIBA European Championship in Istanbul, Turkey, he averaged 9.7 points per game over six tournament games.