Munster hooker Flannery is expected to undergo exploratory surgery on Tuesday after missing the Red Army's Heineken Cup win over Perpignan on Friday night.
Depending on the extent of the damage, the 31-year-old could also be a doubt for Ireland's Six Nations title defence against Italy on February 6.
But Munster team manager Shaun Payne said: "There has been a lot of speculation in the media over the weekend about this but realistically we have to wait until he has had the procedure before we can know for sure."
It is the latest blow for Flannery who was selected for the British & Irish Lions tour to South Africa last summer but had to pull out prior to their departure with an elbow injury.
His absence will allow Munster reserve hooker Denis Fogarty the opportunity to step up for the clash with Irish rivals Connacht on Boxing Day and Ulster on January 2.
And with Rory Best also sidelined, Fogarty, 26, could fight it out with brother John at Leinster and Connacht's Sean Cronin for a spot in the national side.
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