After signing with the Royals, Melendez made his professional debut with the Rookie-levelArizona League Royals where he posted a .262 batting average with four home runs and thirty RBIs over 47 games.[5] He spent 2018 with the Lexington Legends of the Single-ASouth Atlantic League, slashing .251/.322/.492 with 19 home runs and 73 RBIs in 111 games,[6] earning All-Star honors.[7] Melendez spent 2019 with the Wilmington Blue Rocks of the High-ACarolina League and was named an All-Star.[8][9] Over 110 games, he slashed .163/.260/.311 with nine home runs and 54 RBIs.[10] He did not play a minor league game in 2020 since the season was cancelled due to the COVID-19 pandemic. To begin the 2021 season, he was assigned to the Northwest Arkansas Naturals of the Double-A Central.[11] He earned Double-A Central Player of the Month honors for July after batting .333 with 12 home runs over the course of the month.[12] After slashing .285/.372/.628 with 28 home runs and 65 RBIs over 79 games, he was promoted to the Omaha Storm Chasers of the Triple-A East in early August.[13][14] Over 44 games with Omaha, he slashed .293/.413/.620 with 13 home runs and 38 RBIs.[15] His total of 41 home runs for the season led the minor leagues, and he became the first ever catcher to win the Joe Bauman Home Run Award.[16][17]
On November 19, 2021, the Royals selected Melendez's contract and added him to the 40-man roster.[18] He returned to Omaha to begin the 2022 season.[19]
On May 2, 2022, Melendez was a designated hitter for Omaha. In the game, he was on second base and tagged up to third on a line drive by his teammates to right. His manager came up to him and describes to him that he didn't want to tell him this way. He was called up to the majors that day.[20] On May 17, Melendez hit his first career home run during a game versus the White Sox off of lefty pitcher Tanner Banks.[21] On July 4, Melendez had his first career multi-homer game, launching home runs off of Jake Odorizzi and Phil Maton of the Houston Astros.[22]