Kuenn was born in West Allis, Wisconsin, but raised in neighboring Milwaukee, Wisconsin and attended Lutheran High School. He was the only child born to German-Americans Harvey and Dorothy (Wrensch) Kuenn. He once kicked (dropkicked) a 53-yard field goal for Lutheran in a football game, which is tied for the eighth-longest field goal in Wisconsin high school football history. He played collegiate baseball at the University of Wisconsin–Madison, where he was a member of Delta Upsilon fraternity. Signed by Detroit as an amateur free agent in 1952, Kuenn was named the starting shortstop after joining the team late in the season. In his first full season in 1953, he hit .308 with 94 runs and led the major leagues with 209 hits, setting a major league rookie record with 167 singles. He received the American League Rookie of the Year and TSN Rookie of the Year awards. Also in that season, he received the first of his ten consecutive selections to the All-Star Game. On October 29, 1955, he married former Miss Wisconsin 1954, Dixie Ann Sarchet in her hometown of Stevens Point, Wisconsin.

A line drive hitter who hit to all fields, Kuenn showed consistency in the next two seasons, compiling almost identical numbers: .306 with 81 runs and 201 hits in 1954; .306 with 101 runs and 190 hits in 1955. He raised his average to .332 in 1956, surpassed only by Mickey Mantle (.353) and Ted Williams (.345) in the batting race. A year later, he slumped badly to .277. But he rebounded in 1958 with .319, ending third in the league behind Williams (.328) and Pete Runnels (.322), and surpassing Al Kaline, Vic Power, Bob Cerv, Mantle, Rocky Colavito, Minnie Miñoso and Nellie Fox. In that season, he switched to the outfield, where he played all three positions over the remainder of his career.

After winning the American League batting crown in 1959 with a .353 average, Kuenn was traded to Cleveland for Rocky Colavito, who had won the home run title with 42 homers (the trade that is often referred to by Cleveland fans as “the curse of Rocky Colavito”). With the Indians, Kuenn hit .308 in the 1960 season. He finished his career in the National League playing for the Giants, Cubs and Phillies, retiring at the end of the 1966 season.

Kuenn became a Milwaukee Brewers coach in 1972 and served as an interim manager in 1975. He suffered a series of medical complications beginning in the mid-1970s, including heart and stomach surgeries, and in February 1980, he had his right leg amputated just below the knee after a blood clot cut circulation. He returned to coaching only six months after the operation.

In 1982, Kuenn managed the Milwaukee Brewers to their only World Series appearance to date after taking over the team in mid-season. He was selected by the Associated Press as the AL Manager of the Year, after taking the Brewers in June from a 23-24 start to the AL East title with a 95-67 record. Milwaukee then won the AL pennant after rallying from a 2-0 deficit and beating the California Angels in the best-of-five American League Championship Series. They ultimately lost the 1982 World Series to the St. Louis Cardinals in seven games.

Kuenn was fired as manager after the Brewers finished fifth in the AL East with an otherwise respectable 87-75 record in 1983. He compiled a 160-118 managerial record. During his tenure, the hard-hitting Brewers were known as Harvey’s Wallbangers. At the time, their roster included Cecil Cooper, Ben Oglivie, Gorman Thomas, and future Hall of Famers Paul Molitor, Ted Simmons and Robin Yount. After being replaced, he worked as a major league scouting consultant for the Brewers.

Kuenn died from complications from heart disease and diabetes at his home in Peoria, Arizona, in 1988 at the age of 57. The Brewers wore a patch with his initials during the 1988 season to commemorate him. That same year, he was elected to the Wisconsin Athletic Hall of Fame. In 2002, his name was added to the Brewers’ honorarium with a plaque in the concourse circling Miller Park.