Votto suffered the injury after a pitch hit his hand in the fourth inning of Wednesday's game against the Chicago White Sox.
The veteran said postgame that he was surprised that the hit-by-pitch resulted in a broken thumb.
"I was in pain, but I thought I was being a baby," Votto said, according to The Athletic's C. Trent Rosecrans.
Infielder Kyle Farmer replaced Votto after the fifth inning.
The 37-year-old is hitting .226/.305/.425 with five home runs and 17 RBIs in 29 games this season.
While he hasn't had the greatest start offensively, Votto did hit the 300th home run of his career on April 30 against the Chicago Cubs.