Munoz (12-2) was flown to UFC headquarters in Las Vegas last week to meet with physicians. The injury will require the 33-year-old fighter to have surgery, and he said he will be out four to six weeks before he's able to return to training.
UFC president Dana White confirmed the news via Twitter on Tuesday, adding that fellow middleweight contender Michael Bisping will take his place.
"Munoz is injured and out of the FOX fight," White wrote. "Now it's Chael Sonnen vs. Mike Bisping Jan. 28, and the winner will fight Anderson (Silva) for the title."
Bisping (22-3) was originally scheduled to face Demian Maia on the televised portion of the event, which takes place in Chicago. UFC has announced that Maia will remain on the card and face undefeated Chris Weidman.
The British fighter will ride a four-fight win streak into the cage against Sonnen (26-11-1), who is 4-1 in his last five, with the lone loss coming against Silva. The winner is expected to face Silva in his native Brazil this summer.
Brett Okamoto covers mixed martial arts for ESPN.com. Josh Gross of ESPN.com contributed to this story.