The midfielder suffered the knock in Tuesday's 2-0 defeat to Hull City, but Appleton has played down fears that the injury could be serious.
"Obviously he'll get an X-ray and a scan. I don't think it is as bad as we first feared," Appleton told reporters.
"He's come off on a stretcher, it is his ankle, but the doctor seemed to be reasonably confident that it won't be a fracture - but I think he's got a problem in between the tibia and the fibula and the ankle joint. We'll get it looked at and we'll see how he is."
Williamson was making just his second league appearance for the club.