Visnjic was the youngest actor to be chosen for the title role in Shakespeare's Hamlet at the Dubrovnik Summer Theatre Festival in Croatia. Originally cast as Laertes, and understudy to Hamlet, he took over the role when the star dropped out of the production shortly before the first performance. Visnjic portrayed the doomed prince for seven years from 1994 to 2000, winning several Orlando Awards (the equivalent of the Tony Award). During an episode of ER, Luka demonstrated his expertise in the part of Hamlet, by reciting an excerpt from the "To be or not to be" soliloquy in Croatian. In the same episode, he demonstrated his skill in another Shakespeare-related hobby by fencing with Noah Wyle's character, Dr. John Carter.

Prior to ER, Visnjic had small speaking roles in films such as The Peacemaker, Committed and Practical Magic. In 1998 he also appeared in Madonna's music video "The Power of Goodbye", and had a cameo in the movie Rounders. But it was Visnjic's break-out role