Tigers rugby director Richard Cockerill told the club's official website that Parling was hurt during last Saturday's clash between England and New Zealand at Twickenham.
Parling went on as a substitute in that game, as he had done against Argentina seven days previously, after providing bench cover for second-row pairing Joe Launchbury and Courtney Lawes.
"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," 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."
The news is another setback for Leicester and England, with Tigers' powerful Test centre Manu Tuilagi currently recovering from surgery to repair a torn pectoral muscle that threatens his Six Nations participation.
England's opening game in the tournament is against France in Paris on February 1.