Kramer was the 39th player selected in the 1958 NFL Draft, taken in the fourth round by the Green Bay Packers. Two Hall-of-Famers for the Packers were taken in this draft: fullback Jim Taylor of LSU in the second round (15th overall), and linebacker Ray Nitschke of Illinois in the third round (36th overall). Kramer played every game in his rookie season of 1958 but the Packers finished with the worst record (1-10-1) in the 12-team league. In January 1959, the Packers hired a new head coach, Vince Lombardi, the offensive coach of the New York Giants.
With Kramer playing right guard, the Packers won five NFL titles and the first two Super Bowls. Kramer also served as the team's place kicker in 1962, 1963, and part of 1968. As a kicker, he kicked 29 field goals, 90 extra points, for a total of 177 points. He also kicked 3 field goals and 1 extra point in the Packers 16-7 victory over the New York Giants in the 1962 NFL title game. In college at Idaho, he was also a kicker, with Wayne Walker as his long snapper.
During his career, Kramer was often injured. Among these were surgery to remove sizable wood fragments embedded in his abdomen from a teenage accident, and a badly injured ankle suffered in 1961. In all, Kramer played in 129 regular season games; he also had 22 surgeries in 11 seasons, including a colostomy, which he described as "a horror movie that hasn't been made yet." Despite these setbacks, Kramer was selected as an All-Pro five times (1960, 1962, 1963, 1966, and 1967). He was elected to the Wisconsin Athletic Hall of Fame in 1993. He is a member of the NFL's 50th Anniversary All-Time team, and the only member of that team not in the Pro Football Hall of Fame.