Donald, recovering from a bruised tendon in his right index finger, won't accompany the Tribe on its trek through Kansas City and Minneapolis.
"There's no need for it," manager Manny Acta said. "He's not going to be playing, so he's just going to stay back and continue his rehab here."
The infielder, who said the swelling in the finger has improved in recent days, was scheduled to be examined by hand specialist Dr. Thomas Graham on Thursday night.
Donald sustained the injury in the seventh inning of Saturday night's game at Progressive Field, when he took a fastball from Twins starter Nick Blackburn off his right hand while laying down a bunt.
Acta hasn't lost hope that Donald will suit up for the Tribe again this season.
"I don't see why not," he said. "Seven to 10 days is what they diagnosed, so we'll see where he's at after that."