The former Leicester defender was absent on Boxing Day for the 4-2 defeat to Nottingham Forest due to a groin injury.
Whites boss Neil Warnock is hopeful that the problem will clear up with rest and that his skipper will not need surgery.
He told Yorkshire Radio: "He has had a long-standing injury so we are going to see how he gets on with a rest and see if it clears up.
"If it doesn't, we will have to look in other directions to rectify the problem.
"We are optimistic it will just need a bit of a rest. He will not be back for the Hull game but we are hoping he will be OK for the Bolton game."
Midfielder Rodolph Austin (ankle) made a surprise return to the Whites' XI on Wednesday and could play a part once more.
Striker Ross McCormack has had to make do with a place on the substitutes' bench in recent weeks but could be recalled following the heavy defeat at the City Ground.
- Sports & Recreation
- Neil Warnock
- Yorkshire Radio