The Republic of Ireland goalkeeper, 34, damaged the joint for the second time in less than a year during the warm-up for City's Europa League tie against Aris Salonika last week.
Time's up: Shay Given looks to have played his last game for Manchester City
Given is due to be examined in London by a specialist, when he will discover if he needs another operation.
However, it is understood that the surgeon has seen scans of the shoulder and his initial assessment is that Given will need surgery.
That would rule him out until the endof the season, when he will be allowed to leave City after afrustrating time as understudy to Joe Hart.
Boss Roberto Mancini confirmed Sportsmail's exclusive, saying: 'Shay has this problem in his shoulder and I think he needs three months to recover. He has the same injury that he had last year and I think that he needs an operation.
'I am disappointed for him because we have lost a good goalkeeper. Last year we had the problem in the last three games because we lost him to injury and I hope this year it is notthe same.'
No luck of the Irish: Given initially injured his shoulder at the Emirates Stadium last season
Asked if he would recall David Gonzales from his loan spell at Leeds, Mancini said: 'Probably. We can take David from Leeds. We don't have many more options.'
Given's age and his recurring injurywill have an impact on his choices and his fee but Celtic is onepossible destination and former City manager Mark Hughes is keen totake him to Fulham.
Surgery will also deprive Ireland manager Giovanni Trapattoni of his most important player for the Euro 2012 qualifiers against Macedonia next month and possibly in June.
Former Arsenal goalkeeper Stuart Taylor, 30, who has never played a league game for City, will be on the bench on Thursday for the return leg against Salonika.
City will be without influential midfielder Nigel de Jong for last-32 game at Eastlands. The Holland international's injured ankle is only slowly responding to treatment. He is also expected to miss Sunday's Barclays Premier League home game against Fulham.
Man City keeper Given made to wait to discover extent of shoulder injuryI'm disappointed City didn't let me leave in January, admits GivenGoalkeeper Hart in fear of derby axe after slips cost Manchester CityManchester City FC news from across the web Explore more:People: Stuart Taylor, Shay Given, Joe Hart, Mark Hughes, Roberto Mancini Places: London, Leeds, Republic of Ireland, The Netherlands, Macedonia, Ireland