The right-hander was shelved a day after tossing 7 1/3 shutout innings against American League Central-leading Detroit before the Tigers rallied for victory in the ninth against closer Chris Perez.
The stunning loss put the second-place Indians four games off the pace in the AL Central.
Kluber, who has compiled a 7-5 mark for the Tribe this season, lowered his ERA to 3.54 through 19 starts with the effort. He logged 116 strikeouts over 122 innings before going on the DL.
Pitcher Matt Langwell was recalled from Class AAA Columbus to take his spot on the roster.