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. He was signed permanently during the season and was released on 22 April 2010. After Karlsruhe, Drpić had brief spells with AEK Athens in Greece and Volyn Lutsk in Ukraine before returning to Croatia in March 2012, signing for HNK Rijeka.