Zahn was born in Marshall, Minnesota, the son of Zelda, who worked for the YMCA, and Carleton E. Zahn, a retired Missouri Synod Lutheran pastor. He is of German descent.
Zahn spent part of his childhood in Mankato, Minnesota, attending Kennedy Elementary School. After attending Robbinsdale Cooper High School, Gustavus Adolphus College and the Institute for Advanced Theatre Training at American Repertory Theater at Harvard University, his first professional acting role was in Biloxi Blues, a Minnesota production at the Old Log Theater; but his first big break came in 1994, when he was noticed by Ben Stiller, who cast him in his picture, Reality Bites.