The influential Iceland international had to be stretchered from the field during Saturday's 2-0 defeat at Sheffield Wednesday and, although the club are still awaiting official scan results, early indications suggest a break or fracture.
His absence will be a big blow to manager Chris Coleman who is already without fellow midfielder Sammy Clingan until next month as he recovers from a broken toe.
Defender Ben Turner (knee and ankle) and midfielder David Bell (ankle) are not expected to be ready for first-team action after recent injuries and are unlikely to make the trip to the Welsh capital.
Defender James McPake (shoulder) also misses out once again, as does left-back Marcus Hall for family reasons.
New loan signings Chris Hussey and Gary Madine should make Coleman's squad for the encounter which will see former Sky Blues striker Jay Bothroyd come up against his old club.