Schuck started his acting career onstage at Denison University, and after graduation he acted at the Cleveland Playhouse, Baltimore's Centerstage, and finally ended up at the American Conservatory Theater, where director Robert Altman discovered him. Altman cast him in his first theatrical appearance as Captain Walter Koskiusko "Painless Pole" Waldowski, in the 1970 film M*A*S*H, in which Schuck was the first actor ever to say the "F" word in a major motion film. Altman cast him in three more of his films: Brewster McCloud, McCabe & Mrs. Miller, and Thieves Like Us.
The years 1971 - 1977 saw Schuck as Sergeant Charles Enright in McMillan and Wife, while 1976 caught a glimpse of him in the short-lived series Holmes & Yo-Yo as Gregory "Yo-Yo" Yoyonovich. In 1977 he starred as Odell, an overseer in the mini-series Roots. In 1979 he was cast as Frankenstein's Monster in the TV holiday special The Halloween That Almost Wasn't (alternate title: The Night Dracula Saved The World.) He made his Broadway debut in 1979 using the name "John Schuck" as Oliver Warbucks, acting as a replacement in the original Broadway musical comedy Annie, which ran in New York City for a special three-week engagement at the Alvin Theater. It was in 1980 when he was cast as a "regular replacement" in Annie on Broadway, which ran for a year and a half.
It was in 1986 that he was cast as the Klingon ambassador (a role he's well known for in the Star Trek community) in Star Trek IV: The Voyage Home, and in 1991 he played him again in Star Trek VI: The Undiscovered Country. He also appeared in Star Trek: Deep Space Nine (as Legate Parn), Star Trek: Voyager (as Chorus #3), and in Star Trek: Enterprise (as Antaak). He also made an appearance as Draal in Babylon 5, and in 1994 he acted as Ralgha nar Hhallas (call sign Hobbes) in the video game Wing Commander III: Heart of the Tiger, and also acted in Holy Matrimony.
In 2006 he reprised the role of Daddy Warbucks in the Broadway revival of Annie, this time using the name Conrad John Schuck, touring nationally in that role.
He is currently married to his second wife, artist Harrison Houle (his first wife being Susan Bay). He has one son with Susan named Aaron, and two stepsons with Harrison.