ooper, who suffered the injury after coming on for Wales as a replacement against England on Saturday, has been replaced in the squad ahead of Sunday's clash with Scotland by Bath scrum-half Andy Williams.
"Gareth will also have a scan this week, but experience tells us that surgery is probably necessary as a consequence of the dislocation suffered to his right shoulder," said Wales team physio Mark Davies.
"He has previously injured the same shoulder and the necessity for repair would imply that he won't play again this season."
Wales have spent much of this season lurching from one injury crisis to the next.
Ceri Sweeney, who withdrew from the squad to play England with a groin injury, is unlikely to recover in time to be considered for the Scotland game.
"Ceri is currently resting his injury and will undergo a scan this evening to determine the full extent of the damage, but he is unlikely to return in time for the weekend's fixture," said Davies.
Saracens prop Ben Broster has also been invited to join the squad, as cover for Adam Jones who suffered a dead leg during Saturday's 47-13 defeat at Twickenham.
Captain Gareth Thomas, who has been struggling with a knee problem, has returned to a full training programme and number eight Gareth Delve is back in contention after recovering from a hamstring strain which forced his late withdrawal from the England game.
Wales will also have loose-forward Dafydd Jones, centre Gavin Henson and lock Ian Evans suspended for the game against Scotland.