The defender was on the receiving end of a strong tackle from Hull City's David Meyler during Swansea's 3-1 win at the Liberty Stadium on Saturday, with the midfielder being shown a straight red card.
Naughton was forced off as a result of the injury and, while a scan on Saturday ruled out a fracture, the former Tottenham man has suffered ligament damage that will sideline him for up to six weeks.
Angel Rangel will likely replace Naughton in Garry Monk's starting XI as Swansea seek to retain their top-half position in the Premier League.
"It's not good because Kyle has an injury and I don't wish bad on anyone, but from my point of view I always try and be ready so if the manager needs me I'll try my best," the Spaniard told Swansea's official website.
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