Fuller, who is on the verge of signing a new two-year deal with the Kent club, will visit a specialist to discover how long he will be sidelined, and boss Mark Stimson hopes he will return before the end of the season.
Stimson told the club's official website: "We should have a clearer idea when he sees a specialist tomorrow (Friday) but the early signs are not good.
"Hopefully he won't need surgery on it, but only the specialist can tell us that. Then our next question will be how long does the heavy cast need to be on and when can he have a lighter one so he can play.
"There are some casts you can play on with depending on how heavy it is and how dangerous to your opponent. I think he'll be back before the end of the season but he will miss quite a bit of time. Any time without your captain, and someone who is playing so well, is going to be hard."