Schultz was born in Baltimore, Maryland. He is a graduate of Calvert Hall College High School and an alumnus of Towson University, both located in Towson, Maryland. He married former actress Wendy Fulton in 1983 and has a daughter named Ava, who graduated from the Virginia Military Institute in 2009. Schultz is good friends with voice actors John DiMaggio, Kevin Michael Richardson, and Fred Tatasciore as well as former A-Team costar Dirk Benedict.
Schultz's career began with a role in Thin Ice in 1981. That year, he had one-episode rules in Hill Street Blues and CHiPS. From 1983 to 1987, he played 'Howling Mad' Murdock on The A-Team, starring in ninety-seven episodes. Throughout the 1990s, he played brief roles in Babylon 5, Star Trek: The Next Generation, Diagnosis Murder, Touched by An Angel, and Family Guy. His latest major role was on the animated series "Chowder"; he was part of sixty-four episodes as several characters.