Also, the club announced that prospect Danny Salazar, who was recalled from Triple-A Columbus on Wednesday for what was originally going to be a spot start against Detroit, will fill Kluber's spot in the starting rotation.
"Corey's been exceptional," general manager Chris Antonetti said. "It's hard to overstate what he's meant to our team, but at the same time, we have a guy in Danny Salazar that will come up and get an opportunity to pitch.
"He's a really talented player that we think is ready to contribute up here. Now, we'll have to rely on Danny and the other four guys to carry the load until Corey is ready to come back."
Kluber realized something was wrong with his finger during the eighth inning Monday, when he threw a curveball to leadoff hitter Jose Iglesias. He retired Iglesias and allowed a single to Ramon Santiago before exiting the game, in which he held Detroit to six hits and no runs in 7 1/3 innings.
"It was kind of something weird," Kluber said. "I don't know how to describe what I felt. And then it just kind of got stiff, felt like it kind of filled up a little bit."
The Indians ordered an MRI on Tuesday morning, when Kluber woke up and his finger "kind of felt jammed." The results of the exam confirmed a sprain, which will keep Kluber from throwing until his symptoms dissipate. The righty had never spent time on the disabled list before Tuesday.
Through 21 games (19 starts), Kluber is 7-5 with a 3.54 ERA. Over his past 16 outings, he has a 5-3 record and 3.07 ERA.
Kluber's injury helped Salazar find a more permanent spot in the rotation. The Indians will get another look at their No. 6 prospect on Wednesday, and more times after that.
"Before Corey went down," manager Terry Francona said, "we had slotted Danny in this spot, and that was for competitive reasons, because we think he can come up and help us win."
In his only career Major League outing, Salazar limited Toronto to a run and two hits across six innings on July 11. Cleveland toyed with the notion of including him in a temporary six-man rotation down the stretch, but Kluber's injury meant "that probably went out the window," said Francona.
Sturdy contributions from Salazar down the stretch would go a long way in making up for the loss of Kluber. The Indians are confident his absence will not last as long as that of McAllister, partly because the club acted more swiftly in this instance.
"I'm optimistic that Corey will pitch in September," Antonetti said. "We'll have to see how he's feeling. Different people recover at different rates. The most important thing in the first step of the process is making sure he's not feeling any symptoms, not feeling any pain, tightness.
"Once that subsides, then we can start ramping up his throwing."
The Indians were very cautious in handling McAllister. They intend to treat Kluber with the same prudence.
"I don't know exactly what the details to 'symptom-free' means," Kluber said. "I just got to be patient with it until it gets to that point and not try to force it so it doesn't turn into something more serious."