The injury will put Bruce on the 15-day disabled list.
"He said everything went well," general manager Walt Jocketty said of the surgery which was performed by team doctor Tim Kremchek. "It went as expected and the surgery was routine."
Bruce became the 11th Cincinnati Reds to find his way onto the disabled list this season. Unfortunately, it is unknown how the injury occurred.
"I think it's something he's had for a while. It inflamed on him," Jocketty said. "I'm sure he did it playing, but we don't know when."
The two-time All-Star is batting .216 with three home runs, 14 RBIs this season. He was scratched from the starting lineup before Sunday's win over the Brewers because of left knee soreness. He eventually came in to pinch-hit in the bottom of the seventh inning and struck out.
Chris Heisey, who has spent most of his time coming off of the bench, will most likely take over in right field for the time being. He has appeared in 26 games this season and has collected 15 hits including a homerun and six RBIs.
Cincinnati has also had injury problems with speedy center fielder Billy Hamilton who injured his wrist diving for a ball last week. It is unclear whether or not he will be in the lineup on Tuesday against the Boston Red Sox.