I believe this is the same type of injury that Zach McAllister suffered earlier this year, and he missed almost seven weeks. We'll find out more about the exact severity soon, but even if he's out the minimum DL stint, it's a major blow to the team's playoff chances. Next to Justin Masterson, Kluber has been the team's best starter since joining the rotation in late April, and yesterday shut down one of the league's best offenses. No team would be able to replace that type of production. If you look at xFIP (Fielding Independent Pitching), Kluber has been one of the best pitchers in the AL this year:
AL xFIP Leaders
Langwell is likely up here only for today, as tomorrow the Indians will be bringing up Danny Salazar to start. The Indians would likely need to bring up a spot starter for Sunday,which would be the next time Kluber's spot comes up. AAA options include Carlos Carrasco, Trevor Bauer, TJ House or even Daisuke Matsuzaka.
Update: as johnf34 points out in the comments below, because Jimenez is being pushed back already, the Indians wouldn't have to bring up a replacement if they keep Danny Salazar in the rotation. But because Salazar is likely going to be shut down by the end of the month, he's not going to be a permanent solution.
Stay tuned for more information.