Dixon was averaging 4.3 points and 1.8 assists in 36 games with Toronto this season, his second with the Raptors.
Dixon joined Toronto from Portland last year in a trade deadline deal that sent swingman Fred Jones to the Trail Blazers. Dixon asked Raptors general manager Bryan Colangelo to explore trade options after he lost playing time to newcomers Carlos Delfino, Jason Kapono and Jamario Moon.
Toronto will be Brezec's third team this season. The 7-foot-1 Slovenian began the year with Charlotte but was traded to Detroit along with Walter Herrmann in a Dec. 14 deal that sent Nazr Mohammed to the Bobcats.
Brezec, who played alongside Toronto's Rasho Nesterovic for Slovenia at the 2006 world championships, is averaging 1.7 points and 1.7 rebounds in 37 games this season.