Keller was selected 7th overall by the Arizona Coyotes at the 2016 NHL Entry Draft. With Boston's exit from the NCAA tournament he signed a three-year entry-level contract with the Coyotes on March 26, 2017 and played in his first NHL game the next night against his hometown team, the St. Louis Blues. He earned his first NHL point with an assist in the next game, also against the Blues.
Keller was named NHL Rookie of the Month for the month of October after he became the franchise's first rookie to record at least nine goals in one month since Teemu Selänne in March 1993. He also became the first rookie to record 15 points in a month since Selänne and Keith Tkachuk did so in March 1993. On March 21, 2018, Keller broke the Coyotes rookie points record after recording his 54th and 55th of the season in a 4–1 win over the Buffalo Sabres, surpassing Peter Mueller. Keller was again named the NHL Rookie of the Month in March after he led all rookies with 13 assists and 19 points in 17 games and recorded a 10-game points streak, which was the longest by any rookie in the 2017–18 season. Before the conclusion of the regular season, Keller was awarded three team awards; Team MVP, Leading Scorer Award, and the Three Star Award. Keller completed his rookie season with 42 assists and 65 points, leading the team in points and goals, as well as tying for assists. On April 22, 2018, Keller was named one of the finalists for the Calder Memorial Trophy, awarded to the best rookie in the NHL.