Bote grabbed his shoulder after the play at second base in the fourth inning. He was helped off the field and replaced by Patrick Wisdom at third base before the Reds batted in the top of the fifth.
The team said Bote is undergoing further evaluation. He finished 0-for-1 with a run scored.
The Cubs have been hit hard by injuries this month, especially among their position players. Infielders Matt Duffy and Nico Hoerner and outfielders Jake Marisnick and Jason Heyward have been placed on the 10-day injured list since May 10. First baseman Anthony Rizzo has been sidelined by back trouble.
Bote, who is 28, is batting .194 with five homers and 23 RBIs in 49 games.
The Associated Press contributed to this report.