Kapp played college football at the University of California, Berkeley, where he led the Golden Bears to a Pacific Coast Conference championship in 1958 and the Rose Bowl, where they lost to Iowa. This remains California’s most recent Rose Bowl appearance. Kapp was named an All-American, and was also awarded the W. J. Voit Memorial Trophy in 1958 as the outstanding football player on the Pacific Coast. A two-sport athlete and fraternity member of Kappa Alpha Order in college, he also played on the basketball team and was a member of the 1956–57 and 1957–58 squads that won the Pacific Coast championships. He earned a Bachelor of Arts degree in physical education from the university in 1959.

Kapp joined the Calgary Stampeders of the CFL for his rookie season in 1959. The following year, Kapp led Calgary to their first playoff appearance in years. The season was a difficult one, because he injured his knee against the Toronto Argonauts early in the season, but did not miss any games, because he played heavily taped.

The Minnesota Vikings general manager was Jim Finks, who had brought Kapp to Canada in 1959, and their head coach was Bud Grant, who had faced Kapp while coaching the Winnipeg Blue Bombers. Both Finks and Grant thought Joe Kapp would be the best replacement for Fran Tarkenton, who had been traded to the New York Giants. To make this transaction possible, the BC Lions traded all-star defensive lineman Dick Fouts, and future Canadian Football Hall of Fame running back Bill Symons to Toronto for the CFL rights to future Canadian Football Hall of Fame wide receiver Jim Young. They then managed to get Kapp waived out of the CFL. The Vikings managed to get Jim Young waived out of the NFL, which allowed the BC Lions to sign him. The expansion New Orleans Saints wanted Young and it took some work from Finks to keep them from claiming Young. Kapp, now waived from the CFL, was free to sign with the Vikings, who had previously claimed his NFL playing rights from Washington.

In 1961, the BC Lions, then the CFL’s newest franchise, traded four starting players to the Calgary Stampeders for Joe Kapp. The move paid off for the Lions when Kapp led the team to a Grey Cup appearance in 1963. The following season, Kapp led the Lions to their first Grey Cup victory in 1964. However, the Lions proved unable to defend their championship in 1965.

Kapp and fellow Canadian Football Hall of Fame player Angelo Mosca came to blows at a 2011 Canadian Football League Alumni luncheon. The source of the bad blood between Kapp and Mosca is a hit Mosca made on Kapp’s teammate Willie Fleming in the 1963 Grey Cup game. The hit, which Kapp and many others considered dirty, forced Fleming out of the game. Mosca’s Tiger-Cats defeated Kapp’s Lions 21-10 for the 1963 championship.

The Minnesota Vikings in 1965 had drafted running back Jim Young out of Queen’s University in Kingston, Ontario. He had spent the 1965 and 1966 seasons with the Vikings, but wanted to return to Canada. The BC Lions were very interested in acquiring Young, but the Toronto Argonauts had his CFL rights.

Before the 1967 CFL season, Kapp made the decision to return to the U.S. to play pro football. The AFL’s Oakland Raiders, San Diego Chargers, and Houston Oilers were heavily pursuing him.

In 1967, Kapp’s first season in the NFL, he started 11 of 14 games for the Vikings, compiling an unusual record of 3 wins, 5 losses and 3 ties. Kapp completed only 47 percent of his pass attempts with 8 touchdowns and 17 interceptions. Kapp also scored two rushing touchdowns. Of note, the team was winless without Kapp starting at quarterback. The Green Bay Packers won the division (and the Super Bowl).

In 1968, Kapp led Minnesota to their first ever playoff appearance, losing to the favored Baltimore Colts, 24–14. The Colts were upset a few weeks later by the New York Jets in Super Bowl III.

Early in the 1969 season, Kapp tied an all-time record when he threw for seven touchdown passes against the defending NFL champion Colts on September 28. He is tied with seven other players (Sid Luckman, Adrian Burk, George Blanda, Y. A. Tittle, Nick Foles, Peyton Manning, and Drew Brees). Kapp led the Vikings to a 12–2 record, and a berth in Super Bowl IV after defeating the Los Angeles Rams 23–20 in the Western Conference championship game, and the Cleveland Browns 27–7 in the last NFL Championship game ever played. However, he was unable to lead the team to victory in the Super Bowl, as the Vikings lost 23–7 to the Kansas City Chiefs. In 1970, the NFL and AFL consummated the merger that had been agreed to in 1966, and the NFL Championship game was retired after 37 editions and 50 years of NFL competition. On July 20, 1970, Sports Illustrated dubbed Kapp “The Toughest Chicano” on the cover of its weekly magazine. He received the team MVP, but refused the team MVP award, saying, “There is no one most valuable Viking. There are 40 most valuable Vikings.”

With the top pick in the 1971 NFL Draft, the Patriots selected quarterback Jim Plunkett of Stanford, the winner of the Heisman Trophy. Kapp reported to the newly-renamed New England Patriots’ training camp in 1971, refused to sign a standard contract, and departed. The headlines in the Boston papers read “KAPP QUITS!”. After this incident Kapp never played again; his 12-year career as a professional football player was over.

Although Kapp was not awarded any damages, in 1977 the rules at issue in the Kapp case were later revised, a new system was instituted, and a multimillion-dollar settlement was made between the NFL and the NFL Players Association.

In December 1981, Kapp made a promise to the football team that he would not consume any of his favorite alcoholic beverage, tequila, until the Golden Bears reached the Rose Bowl, which they did not under Kapp; indeed, as of 2020, the Golden Bears have yet to return to the Rose Bowl — they were Pac-10 co-champions in 2006 but a loss to USC sent them to the Holiday Bowl instead. (In a 1994 interview, Kapp stated that he had resorted to drinking rum instead.

In 1982, Kapp was hired as the head football coach at his alma mater, the University of California, Berkeley. He had never coached before. In his first year as head coach, he was voted the Pacific-10 Conference Coach of the Year.

Kapp’s first season as head coach in 1982 concluded with The Play, the famous five-lateral kickoff return by Cal to score the winning touchdown on the final play of the Big Game against archrival Stanford.

During the 1986 season, the Bears lost to Boston College, defeated Washington State, then lost to San Jose State. Following an embarrassing 50–18 loss at Washington on October 4, Kapp expressed frustration unzipping his pants in front of the Seattle media. He was notified that he would be released after the Big Game, played in Berkeley. The Bears responded to the student section’s pre-game chants of “Win one for the zipper” by beating the Gator Bowl-bound #16 Cardinal 17–11, which gave Kapp a 3–2 record in the Big Game. He was carried off the field by his players, amid chanting from the student section, “We want Kapp!” echoing a cheer from his playing days with the Boston Patriots.

In an effort to recapture their past glory, the BC Lions of the Canadian Football League (CFL) hired Kapp as the team’s new general manager in 1990. Kapp’s tenure was marked by his tendency to recruit ex-NFL players such as Mark Gastineau whose best football days had passed. Kapp was fired eleven games into the Lions’ schedule, his most valuable legacy was the signing of quarterback Doug Flutie, who would blossom into a star in the CFL during the 1990s.

In 1992, Kapp was named the head coach of the Arena Football League’s Los Angeles Wings, but the franchise never came into existence in Los Angeles, and moved to Sacramento as the Attack. The franchise went 4–6 under Kapp, losing in the first round of the playoffs to the Detroit Drive. After the season, the franchise moved to Miami, Florida.

Kapp lives in Los Gatos, California, and makes himself available as a guest speaker. He has a wife and four children and four grandchildren. He was one of the owners of Kapp’s Pizza Bar & Grill in Mountain View, California, which contained memorabilia from his career and closed in 2015. His son, Will, followed in his footsteps as a fullback at UC Berkeley. In 2015, grandson Frank Kapp, continued the Cal football tradition as a freshman tight end with the Golden Bears.

In February 2016, the San Jose Mercury News reported that Kapp was suffering from Alzheimer’s disease.