Malkovich was born in Christopher, Illinois, and grew up in Benton, Illinois. His father, Daniel Leon Malkovich (1926–1980), was a state conservation director and publisher of Outdoor Illinois, a conservation magazine. His mother, Joe Anne (née Choisser; 1928–2009), owned The Benton Evening News, as well as Outdoor Illinois. Malkovich has three younger sisters and an older brother. His paternal grandparents were from Ozalj in Croatia, and
according to his mother they were of Montenegrin ancestry. His mother was of French, German, Scottish and English ancestry.
Malkovich attended Logan Grade School, Webster Junior High School, and Benton Consolidated High School. During his high school years, he appeared in various plays and the musical Carousel. He was active in a folk gospel group, singing in area churches and community events. As a member of a local summer theater/comedy project, he co-starred in Jean-Claude van Itallie's America Hurrah in 1972. Upon graduating from high school, he entered Eastern Illinois University, and then transferred to Illinois State University, where he majored in theater.