It is not yet known which knee Carwin injured. UFC is seeking an opponent for Nelson.
"Wow! It never ends; Carwin blew his knee out," White said on Twitter.
Carwin has been out of action since June 2011, when current heavyweight titleholder Junior dos Santos defeated him by unanimous decision.
After that loss, Carwin (12-2) injured his back during a training session. He underwent surgery to repair the injury.
Less than a week ago, Nevada State Athletic Commission executive director Keith Kizer said Carwin and Nelson had passed prefight drug tests for their December fight.
Carwin and Nelson were opposing coaches on Season 16 of "The Ultimate Fighter." They directed harsh words toward one another for several months.
Their fight was scheduled to headline TUF 16 Finale at Hard Rock Hotel & Casino in Las Vegas.