The 24-year-old suffered suspected cruciate ligament damage in the closing stages of the npower Championship victory at Cardiff on Saturday.
"It doesn't look good," Forest manager Billy Davies told the club's official website.
"We sent Dexter to see some specialists. We're still waiting on some scans and reports but what we do know is that a hell of a lot of damage has been done.
"It certainly will be a lengthy period that Dexter will be missing. It certainly looks like he will have to have more than one operation."