"Forrest has (an) MCL tear and (an anterior cruciate ligament) strain," White said on Twitter. "The saga continues at UFC."
Griffin (19-7) was originally scheduled to fight former top middleweight contender Chael Sonnen at the Dec. 29 event, which will be held in Las Vegas.
But Sonnen was removed from that fight after landing a coaching stint on next season's version of 'The Ultimate Fighter' opposite current 205-pound titleholder Jon Jones.
Sonnen and Jones will settle their differences at UFC 158 on April 27, 2013, in Newark, N.J.
Davis (10-1 with one no-contest) submitted Wagner Prado in the second round of their rematch on Oct. 13 at UFC 153. The first meeting between them ended in a no-contest after Davis accidentally poked Prado in the eye during first-round action.
UFC has not yet determined whether Davis will remain on the Dec. 29 card.
Griffin is the latest high-profile fighter to drop out of the event. Last month, middleweight contender Chris Weidman withdrew from a showdown against Tim Boetsch after falling victim to a shoulder injury.