Manager Mark Stimson told BBC Radio Kent: "He was just shielding the ball out, the lad was trying to get the ball of him and caught his arm.
"There was no intent, just one of those freak accidents.
Fuller, 26, missed two months of last season with pneumonia but recovered to lift the trophy at Wembley when the Gills beat Shrewsbury in the League Two play-off final.
He has only missed two games this season, one when he was suspended and the other when he was one of many players caught in traffic on the way to the away match at Orient in December.
Stimson now has to assess his captaincy options with Danny Jackman the most likely candidate after he took the armband after Fuller went off on Tuesday.
Chris Palmer looks most likely to replace Fuller at right-back.
There is commentary of Carlisle v Gillingham on Saturday on BBC Radio Kent.
Source: BBC Sport
Source: BBC Sport