Miniussi turned professional in 1984. He started playing tennis at the Adrogué Tennis Club and he also represented his native country as a lucky loser at the 1992 Summer Olympics in Barcelona, where he was defeated in the first round by France's Fabrice Santoro. In the doubles competition Miniussi claimed the bronze medal alongside Javier Frana. The right-hander won one career title in singles (São Paulo, 1991). He reached his highest singles ATP-ranking on 18 May 1992, when he became the number 57 of the world.