Visnjic is married to Croatian sculptor Eva Visnjic (born Ivana Vrdoljak), the daughter of filmmaker Antun Vrdoljak. They reside in Los Angeles, and maintain a home and a boat on the Croatian island of Hvar. The couple have three children: Tin, adopted in 2007 and named after Croatian poet Tin Ujević, Vivien, born in 2009 and adopted in 2013, and biological son Vigo, born in 2011. Visnjic has acknowledged paternity of a daughter, Lana, born in 2007.

Visnjic has been active in the American and European animal rights movements, and appeared in photographs alongside his dog Bugsy in PETA’s first Eastern European anti-fur campaign. He is currently a representative for both the International Fund for Animal Welfare and an Animal Friends Croatia, as well as providing assistance to a number of small animal-rescue organizations in southern California. He has also supported a number of medical institutions in Croatia through the donation of money or equipment. Visnjic recently appeared on the nationally broadcast American benefit program Stand Up to Cancer. He also served as one of the faces of ER on NBC’s long-running The More You Know campaign, appearing in public service announcements discussing topics such as family time and tolerance.