Manager Eric Wedge said Elarton is out "indefinitely."
Elarton, promoted from Triple-A Buffalo in late May, made eight appearances as the long reliever out of the Tribe's bullpen. He went 0-1 with a 3.52 ERA over 15 1/3 innings.
Anthony Castrovince is a reporter for MLB.com.
This story was not subject to the approval of Major League Baseball or its clubs.