Influential midfielder Abdi picked up a groin strain in the warm-up prior to last weekend's surprise 2-1 home defeat to Blackpool and will again miss out at Oakwell.
Goalkeeper Almunia, meanwhile, has missed the last three games with his hamstring injury and continues to sit out ahead of the forthcoming international break.
On-loan Chelsea midfielder Chalobah was also a big miss against the Seasiders last Saturday but he has shrugged off his hamstring problem and is set to go straight back into boss Gianfranco Zola's starting XI.
Defender Fitz Hall is another player who has overcome a hamstring complaint but his lengthy spell on the sidelines means he is unlikely to be thrown immediately back in against Barnsley.
Neuton (dislocated shoulder), Tommie Hoban (ankle) and John Eustace (back) continue to miss out.