Fichtner was born on Mitchel Air Force Base on Long Island and raised in Cheektowaga, New York, a suburb of Buffalo. He is the son of Patricia A. (née Steitz) and William Frederick Fichtner. He has German ancestry.
He graduated from Maryvale High School in 1974. After graduating from Farmingdale State College in 1976 with an associate degree in criminal justice, he attended the College at Brockport, State University of New York and earned a Bachelor of Arts degree in criminal justice in 1978. In an interview with Michael Rosenbaum, Fichtner recalled he took a theatrical improvisation class initially to fill a fine arts requirement, and the professor recommended he consider taking further acting classes. He then studied at the American Academy of Dramatic Arts in New York.
On May 18, 2008, Fichtner received an Honorary Doctorate of Humane Letters from Farmingdale State College. In his acceptance address, he credited Farmingdale admissions counselor Don Harvey with his decision to study acting. Harvey, who became a lifelong friend, took Fichtner to his first Broadway show.