Vujanić started his professional career with Crvena zvezda (Red Star Belgrade), in 1999. After two seasons at the club, he signed with Partizan Belgrade, in the summer of 2001. In the 2002 NBA draft, Vujanić was selected with the 36th overall pick, by the New York Knicks, but later, his draft rights were traded to the Phoenix Suns.[1] However, he decided to stay with Partizan for one more season,[2] and he was the top scorer of the EuroLeague's 2002–03 season, averaging 25.8 points per game. In the summer of 2003, he moved to the Italian League, and signed a three-year deal with Skipper Bologna.
Vujanić ended up never playing in an NBA game and he is 1 of 9 players from the 2002 NBA Draft to never play a game in the league.