Kuemper played three seasons with the Red Deer Rebels, winning the Del Wilson Trophy in the 2010–11 season as the WHL's top goaltender, as well as the CHL Goaltender of the Year with 45 wins, a goals against average of 1.86 and a save percentage of.933. On May 26, 2011, Kuemper signed a three-year, entry-level contract with the Minnesota Wild. On October 13, 2011, he was loaned to the Ontario Reign of the ECHL. Kuemper was later recalled by the Wild on November 12, 2011. Kuemper was recalled by the Wild on February 12, 2013. After then-backup goaltender Josh Harding stated that he had been feeling ill symptoms due to complications from his multiple sclerosis treatment, the Wild recalled Kuemper to start in net the same night to relieve Harding and the team's starting goaltender, Niklas Bäckström. Five days later, on February 17, Kuemper made 29 saves on 31 shots to earn his first career NHL win against the Detroit Red Wings. On May 1, 2013, Kuemper was again recalled by the Wild to serve as a backup for Josh Harding, who was starting as a result of an injury to Niklas Bäckström. On May 7, Kuemper made his Stanley Cup playoff debut when he replaced Harding, who had suffered a left leg injury in the first period of a game against the Chicago Blackhawks. In the next season's playoffs, in 2014, Kuemper started in Game 3 of the Wild's Western Conference Quarter-finals matchup against the Colorado Avalanche, replacing Ilya Bryzgalov. Kuemper recorded a shutout in the game, and continued to start for the Wild until sustaining an injury in the third period of Game 7 of the same series. Bryzgalov replaced Kuemper again and was credited with the win upon Minnesota's overtime victory later that game. The following season, Kuemper opened as Minnesota's starter with Bryzgalov departed and Harding unable to play. However Kuemper struggled, and Minnesota traded for Devan Dubnyk, who immediately became the starter. Kuemper and Niklas Bäckström finished out the season splitting time as Dubnyk's backup. On July 1, 2017, having left the Wild as a free agent, Kuemper agreed to a one-year, $650,000 contract with the Los Angeles Kings. In the 2017–18 season, Kuemper excelled in the backup role with the Kings, recording 10 wins in 19 appearances. On February 21, 2018, Kuemper was traded to the Arizona Coyotes in exchange for goaltender Scott Wedgewood and forward Tobias Rieder. Kuemper was immediately re-signed to a two-year, $3.7 million contract extension by the Coyotes. With Antti Raanta injured for most of the 2018–19 season, Kuemper appeared in a career-high 55 games; he posted a 27–20–8 record for the team. On October 2, 2019, the Coyotes signed Kuemper to a two-year, $9 million contract extension.
