The two pitchers were previously sent home to quarantine after violating COVID-19 protocols by going out together Saturday night in Chicago.
Clevinger and Plesac will continue to accrue service time and receive pay while on the restricted list, according to Mandy Bell of MLB.com. The team can activate them at any time.
Indians All-Star shortstop Francisco Lindor believes it's important to be selfless during the coronavirus pandemic.
"We have to sit and look ourselves in the mirror," Lindor said Tuesday, according to Zack Meisel of The Athletic. "And it's not about the person we see in the mirror. Its who's behind you. The other people. It's not about that one person. It's about everybody around you: the family members, the coaching staff, (Carlos) Carrasco, all the players on the teams that are high-risk."
Adam Plutko will take Clevinger's spot in the rotation and start Tuesday night against the Chicago Cubs.
Prior to the season, Indians outfielder Franmil Reyes was sent home from training camp for attending a party without a mask. Reyes and Plesac both issued public apologies after their respective actions.