The injury means he will miss Leinster's final two fixtures - against Benetton Treviso and Edinburgh Rugby - as they aim to cement their place in the top six.
But Cronin could be back in time for Ireland's World Cup build-up, the hooker having come off the bench in all of his country's games this year.
In the statement published on Wednesday, Leinster said: "After medical advice, Sean Cronin has this afternoon undergone surgery to repair damage to a tendon in his shoulder.
"The operation has gone well, but Sean will miss the rest of the Leinster Rugby season, which involves games against Treviso and Edinburgh in the GUINNESS PRO12.
"The expected rehabilitation period is 12 weeks."
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