The major league leader with 10 wins, Civale left in the fifth inning of Monday night's win over the Chicago Cubs.
The pitcher is scheduled to be examined by hand specialist Dr. Thomas Graham on Wednesday.
"My guess is we will need to make a roster move," manager Terry Francona said Tuesday. "Because of tomorrow's day off, we can let him get looked at first. But I think we're prepared that he's going to miss some time."
Civale had a 3-2 count on Eric Sogard with two out when he was visited by Francona and a trainer. The trainer examined Civale's right hand before the pitcher was removed.
"He's pretty sore," Francona said. "He says he feels like he jammed it, which obviously he didn't. But that's the feeling. That's what he said it feels like."
The Indians had won six of eight and trailed the AL Central-leading Chicago White Sox by two games through Monday.