McKenzie made his NHL debut in 1958–59 with the Chicago Black Hawks. The following season he moved on to the Detroit Red Wings, where he lasted two years. He was then demoted again to the minors, where he played most of three seasons in the American Hockey League with the Hershey Bears and the Buffalo Bisons, and was named to the league's First All-Star Team in 1963. He returned to the NHL and the Black Hawks in 1963–64, and two years later played for the New York Rangers for part of the 1965–66 season, halfway during which he was traded to the Rangers' arch-rivals, the Boston Bruins.