[6] In 2017, McKenzie played for the Lynchburg Hillcats (A league) where he posted a 12–6 record with a 3.46 ERA in 25 games started.

[12] On August 22, 2020, McKenzie made his major league debut against the Detroit Tigers, striking out ten batters in six innings; McKenzie's 10 strikeouts in his debut performance is the second most by an Indians pitcher in their first major league start.

[13][14] With the 2020 Cleveland Indians, McKenzie appeared in 8 games, compiling a 2–1 record with 3.24 ERA and 42 strikeouts in 33+1⁄3 innings pitched.

On May 22, 2021, McKenzie was optioned to the Triple-A Columbus Clippers after compiling a 1–3 record, a 6.89 ERA, and 30 walks over 31+1⁄3 innings.

McKenzie was demoted again after a poor outing on June 12, due in great part to his high rate of walking batters.

[17] He was recalled for a spot start on July 9, in which he pitched seven shutout innings, giving up just one hit and one walk, while striking out nine Kansas City Royals batters.