Clevinger is the second Indians pitcher in as many days to be cited by the team for violating protocol in Chicago. Zach Plesac had to drive back to Cleveland in a rental car on Sunday before the Indians wrapped up their series against the White Sox after he left the team hotel to go out Saturday.
Clevinger accompanied Plesac when they went out on Saturday in Chicago, a source told ESPN's Jeff Passan. Clevinger flew home with the team, which did not know about his violation before departure.
In a statement Monday, the Indians said Clevinger will go into quarantine and undergo testing while away from his teammates. Clevinger, who is 1-1 with a 3.24 ERA, and Plesac will have to test negative for COVID-19 twice in 72 hours before they'll be allowed to rejoin any team activities.
Both players are being counted on as part of a strong Cleveland pitching staff that has carried the club through 17 games.
The Indians -- and other Major League Baseball teams -- have established codes of conduct to mitigate possible spread of the highly contagious coronavirus.
Last month, Clevinger said he was in favor of the team having guidelines to keep players in check.
"This isn't going to be a 'run to daddy' kind of thing. We're going to handle it in-house. This is a player discipline thing. Keep the coaches, front office kind of out of it,'' he said on July 30. "It puts a little extra accountability, kind of. Just having that trust in your teammates is a big thing. It's a big thing on the field. If you feel your teammate doesn't trust you off the field, how are you going to feel like he trusts you when you get between the lines?''
Clevinger and Plesac could face additional discipline from the Indians, who have been proactive during baseball's restart. They quarantined slugger Franmil Reyes after learning that he didn't wear a mask or practice social distancing while attending a July 4 party.
Team president Chris Antonetti and manager Terry Francona, who has been away from the team for the past eight games while dealing with a gastrointestinal issue, are expected to address Clevinger's situation Tuesday.
Adam Plutko (1-0) will start Tuesday's series opener against the Cubs in Cleveland.
The Associated Press contributed to this report.