Bote got hurt before Friday's 17-13 loss to the White Sox. The ball was obscured by some white lettering in foul territory at Guaranteed Rate Field.
The move with Bote was made retroactive to Thursday.
Manager David Ross said the same thing happened to him during his playing career.
"It messed my ankle pretty good, and he was the same," Ross said. "Watch the replay, it's pretty nasty how hard he rolled his ankle.
"Got some test results back and it's a significant sprain that we'll have to treat and try to get him back as soon as we can. No timetable at the moment."
The 28-year-old Bote is batting .202 with eight homers and 32 RBI in 78 games for the fourth-place Cubs. He missed time earlier in the year with a dislocated left shoulder.
Asked if the ankle injury could sideline Bote for the rest of the season, Ross reiterated that he didn't want to put a timetable on his return.
"I know he felt better today, bouncing back," Ross said.
The Cubs also brought up infielder Alfonso Rivas and right-hander Scott Effross from Triple-A Iowa. Pitchers Ryan Meisinger and Jake Jewell were designated for assignment.
Rivas and Effross are looking for their major league debuts.
The 24-year-old Rivas was selected by Oakland in the fourth round of the 2018 amateur draft out of the University of Arizona. He was traded to the Cubs for infielder Tony Kemp in January 2020.
Rivas is primarily a first baseman, but he also has played the corner outfield spots. He hit .284 with four homers, 32 RBI and a .405 on-base percentage in 58 games for Iowa.
"Fonzy made an impression last spring training, his first with us," Ross said. "Just a smooth glove over there. Controls the strike zone really well. Probably more of a line-drive hitter more than a power hitter, but he's having a good season."