McAllister, who hasn't won since April 21, is 3-6 with a 5.91 ERA in 14 starts. He won his first three decisions, but is 0-6 with a 7.89 ERA in his last 10 starts.
McAllister missed six weeks this season because of a sore back.
With the exception of staff ace Corey Kluber, Cleveland's starting pitchers have struggled all season. Kluber is the only remaining member of the rotation that began the season. Justin Masterson, the team's opening-day starter, was traded to St. Louis on Wednesday.
The Indians recalled outfielder Tyler Holt from Columbus before Friday's game against Texas. Chris Dickerson, who injured his left knee Thursday, is expected to miss a couple of days.