A left-handed batter, Kubek signed his first professional contract with the Yankees and rose rapidly through the team's farm system. He was 21 years old when he played his first game in Major League Baseball in 1957, and—except for one year (1962) spent largely in the U.S. military—remained with the Yankees until his retirement due to a back injury at the close of the 1965 season. In his prime he formed a top double play combination with second baseman (and roommate) Bobby Richardson on an infield that also featured third baseman Clete Boyer.