The squirrel raced in from right field and reached the area around the pitcher's mound, forcing the umpires to halt play. The squirrel, which was cheered by the Progressive Field crowd, ran into foul ground and headed behind home plate but quickly returned to fair territory.
Twins manager Paul Molitor left the dugout to speak with plate umpire C.B. Bucknor, and Twins pitcher Jose Berrios threw his arms up in frustration.
Several members of the grounds crew chased the squirrel down the right-field line before it finally hopped into the stands, allowing play to continue.
"I still can't figure that out, how long they were going to let that guy run around out there before someone got him," Molitor said.
The squirrel's presence didn't help the Indians. The inning ended when Michael Brantley flied out on the second pitch after the delay.
The Twins won the game 4-1.
"Those type of things are funnier when you're ahead," Indians manager Terry Francona said.
Information from The Associated Press was used in this report.