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, and later that year he had one-episode roles in Hill Street Blues and CHiPS. From 1983 to 1987, he played 'Howling Mad' Murdock on The A-Team, starring in ninety-seven episodes.