Menez spent his first professional season with the Arizona League Giants, Salem-Keizer Volcanoes and San Jose Giants, pitching to a combined 4–1 record and 4.22 ERA in 53.1 innings pitched between the three teams. He pitched in 2017 with San Jose, going 7–7 with a 4.41 ERA in 23 games (22 starts), and in 2018 with San Jose, the Richmond Flying Squirrels and the Sacramento River Cats,[5] compiling a combined 9–10 record with a 4.46 ERA in 28 total starts with 171 strikeouts in 135.1 innings (averaging 11.4 strikeouts per nine innings).
He started 2019 with Richmond and was promoted to Sacramento during the season.[6][7] Between the two teams, in 2019 he was 6–4 with a 3.79 ERA in 23 games (22 starts) in which he pitched 121 innings and struck out 154 batters (averaging 11.5 strikeouts per nine innings).[8]
On July 21, 2019, the Giants selected Menez's contract and promoted him to the major leagues.[9] In his major league debut that day, he pitched five innings while allowing 2 runs and recording six strikeouts.[10] In 2019 for the Giants he was 0–1 with a 5.29 ERA in eight games (three starts) covering 17 innings in which he struck out 22 batters.[8]
In 2020 for the Giants, Menez pitched to a 2.38 ERA with 8 strikeouts in 11.1 innings of work.[11]
On August 4, 2021, Menez was designated for assignment by the Giants.[12] Menez was outrighted to Triple-A Sacramento on August 7.[13]
Chicago Cubs
On December 8, 2021, the Chicago Cubs selected Menez in the minor league phase of the Rule 5 draft.[14] He was assigned to the Triple-A Iowa Cubs to begin the 2022 season.
On May 9, 2022, Menez was selected to the 40-man and active rosters.[15] After pitching a scoreless inning in a loss to the Arizona Diamondbacks, he was optioned back to Triple-A Iowa. On June 4, Menez was designated for assignment by Chicago after Caleb Kilian had his contract selected.[16] He cleared waivers and was sent outright to Triple-A Iowa on June 6.[17]
Hokkaido Nippon-Ham Fighters
On June 24, 2022, Menez announced via Instagram that he would be signing with the Hokkaido Nippon-Ham Fighters of Nippon Professional Baseball (NPB).[18][19][20] Fighters manager Tsuyoshi Shinjo said regarding Menez's acquisition that he may come to Japan "in a week".[21] In 18 appearances for the Fighters, Menez recorded a 1.08 ERA with 28 strikeouts in 25.0 innings pitched.
In 2023, Menez pitched in 12 games for the Fighters, logging a 3.16 ERA with 19 strikeouts in 25+2⁄3 innings of work. On July 1, 2023, Menez was released by Hokkaido.[22]
On March 23, 2024, Menez signed with the Diablos Rojos del México of the Mexican League.[24] In 31 games (7 starts), he compiled a 4–2 record and 4.25 ERA with 45 strikeouts across 53 innings of work. With the team, Menez won the Serie del Rey.[25]