 Drpić rose through the youth ranks of Dinamo and became a consistent performer in the first squad.He debuted for the first team in a UEFA Champions League qualifiers return match at A.C. Milan on 9 August 2000, and was one of the key figures in Dinamo's squad in the upcoming seasons.Dinamo loaned Dino to Karlsruher SC in 2008–09 winter transfer window following a scandal in which it was revealed that he and his Playboy model wife Nives Celzijus had sex on the grass at Dinamo's ground.