On 6 July 2019, Šarić, along with the draft rights to Cameron Johnson, were traded to the Phoenix Suns in exchange for the draft rights to Jarrett Culver, completing a trade set on draft day. On 24 November, Šarić scored 18 points and grabbed a career-high 17 rebounds in a 116–104 loss to the Denver Nuggets. He later matched his career-high of 17 rebounds, scoring 19 points this time around, in a 121–119 overtime loss to the San Antonio Spurs on 14 December in Mexico City. After losing his starting spot to Cameron Johnson in the 2020 NBA Bubble during the scrimmage games, Šarić returned as a starter on 10 August, getting 16 points and 9 rebounds in a blowout 128–101 win over the Oklahoma City Thunder. The Suns eventually ended their season with an 8–0 run in the bubble.