Born in the small coastal town of Sivinik on the Adriatic, Visnjic began his acting studies while still a teenager. After completing the required military service in the Yugoslavian army, the Balkan war broke out and he briefly served in the Croatian army.
Leaving the military, Visnjic joined the Croatian National Theatre. Cast as Laertes in a production of "Hamlet", the 21-year old actor assumed the title role when the actor originally cast fell ill. He scored a success with his performance and went on to play the role in throughout Croatia. He found work in local TV productions and landed a Tuborg beer commercial that aired in Europe.
Small roles in the American TV-movie "Alistair MacLean's 'Night Watch'" (USA Network, 1995) and in the feature "The Peacemaker" (1997) followed before Winterbottom cast him as Risto. Subsequently, he appeared as Nicole Kidman's abusive boyfriend in "Practical Magic" (1998) before joining the cast of NBC's hit medical drama "ER" in fall 1999 as pediatrician Dr. Luka Kovac.
Following his "ER" breakthrough, Visnjic appeared in a succession of small films, including "Committed" (2000), "The Deep End" (2001), the UK thriller "Doctor Sleep" (2002) and the Croatian-made films "The Last Will/Posljednja volja" (2001) and "Duga Mracna Noc" (2004), also serving as a producer on the latter two. He also took on the role of "Spartacus" for a 2004 TV remake of the classic film, and received his first major US starring role on the big screen, playing Jennifer Garner's potential love interest in the comic book actioner "Elektra" (2005).