The right-hander will start at home against Detroit. He has been working out at the Indians' alternate training site in Eastlake, Ohio.
The Indians announced McKenzie as Saturday's probable before Thursday night's game against the Pirates.
McKenzie, 23, missed last season because of a shoulder injury after pitching at Double-A Akron in 2018. He has gone 26-16 with a 2.68 ERA in 60 minor league games over four seasons.
McKenzie was a supplemental first-round draft pick in 2015.
The call-up of McKenzie means that Zach Plesac will not pitch this weekend in Detroit.
Plesac and pitcher Mike Clevinger were sent to the alternate site last week. They were found to have broken COVID-19 protocol by leaving the team hotel the previous weekend in Chicago.
Plesac was scheduled to pitch a simulated game Thursday. Clevinger pitched five innings in the same scenario Wednesday.
First-base coach Sandy Alomar Jr., who has been running the Indians while manager Terry Francona deals with a gastrointestinal ailment, was asked what advice he would give McKenzie.
"Just be yourself, trust yourself," said Alomar, a six-time All-Star catcher for Cleveland. "It's a different level but you've still got to throw strikes and do the things that made you successful in the minor leagues."