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.