He starred in the British film Doctor Sleep (2002), alongside Shirley Henderson and Miranda Otto. While starring on ER, Višnjić worked on other projects. By season 14, however, he was only making a limited number of appearances, before completely leaving the show early in season 15 (15x03: "The Book of Abby").
It was his role as Risto, the Bosnian driver in Welcome to Sarajevo that led then-producer Jack Orman to offer him a role as a doctor to replace the departing George Clooney in the sixth season of ER in late 1999, eventually becoming the show's male lead by the start of season 12, having taken over from the departing star Noah Wyle, who left after the finale of season 11.
In 1998, he appeared in Madonna's music video " The Power of Good-Bye", and had a cameo in the movie Rounders. Višnjić also had small speaking roles in films such as The Peacemaker, Committed and Practical Magic. Prior to ER, he found work in local TV productions and landed a Tuborg beer commercial that aired in Europe. During an episode of ER, he demonstrated his expertise in the part of Hamlet, by reciting an excerpt from the " To be, or not to be" soliloquy in Croatian. He portrayed the doomed prince from 1994 to 2000, winning several Orlando Awards (the equivalent of the Tony Award). 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. Višnjić was the youngest actor to be chosen for the title role in Shakespeare's Hamlet at the Dubrovnik Summer Theatre Festival. After leaving the army, he moved to Zagreb to study at the Academy of Dramatic Art. Only weeks after his military discharge in 1991, as Yugoslavia began to dissolve, he joined the nascent Croatian Ground Army. In 1990, at the age of 18, Višnjić served one-year of obligatory military service in the Yugoslav People's Army as a paratrooper. He appeared in plays throughout his childhood and made his screen debut at the age of 16 in the controversial Yugoslav film, Braća po materi (1988), playing a young Ustasha. His father, Željko, was a bus driver, and his mother, Milka, worked in a market. He has one sibling, an elder brother, Joško.
Višnjić was born in Šibenik, SR Croatia, SFR Yugoslavia.