The bout was supposed to co-headline UFC 170, which takes place Feb. 22 at Mandalay Bay Events Center.
UFC president Dana White confirmed Evans' injury to ESPN.com on Wednesday, following an initial report by Yahoo! Sports. UFC co-owner Lorenzo Fertitta told ESPN.com the bout would be rescheduled to a future date, based upon Evans' recovery.
The former light heavyweight champion is expected to miss approximately four weeks.
The fight could land on UFC 172 on April 26 in Baltimore or UFC 173 on May 24 in Las Vegas, according to Fertitta.
"We haven't decided which card yet because we need to wait a few weeks to see how Rashad is progressing," Fertitta said. "Doing the math, it would either be Baltimore or Memorial Day in Vegas."
Hours before the news, Evans (19-3-1) appeared on a UFC media conference call to promote the fight. Evans' wrestling coach Kenny Monday offered few details on the injury, other than to confirm it happened while training.
A welterweight bout between Rory MacDonald and Demian Maia is expected to move into the UFC 170 co-main event. A female bantamweight title fight between Ronda Rousey and Sara McMann is scheduled to headline.