"Geoff suffered some damage in the shoulder during England's match against New Zealand last Saturday and, after taking medical advice this week, he has had an operation to repair it," Tigers boss Richard Cockerill said.
"The prognosis is that he is likely to be out for three months which is obviously very disappointing for Geoff and also for us with all the other injuries we've had this season.
"But we will have to deal with it and we've got some good cover in the squad. We want Geoff to have a trouble-free recovery and to get himself right so he can rejoin the squad later in the season."
Parling played in the Tigers' opening two European matches in October, against Ulster Rugby and Benetton Treviso, but will now miss the final four games as the English Premiership giants attempt to reach the quarter-finals from Pool 5.