Moody, who toured New Zealand with the Lions six years ago, moved to The Rec from Leicester Tigers at the beginning of last season but injury and international commitments have limited the 33-year-old to just 13 league appearances and four Heineken Cup games for his current club.
"Lewis is going to be out for 12 weeks," said Bath coach Brad Davies.
"I'm just gutted for the player himself. He came back enthusiastic in training but I'm sure he's going to give loads off the field now to keep himself occupied.
"It's disappointing but what can you do? He's always played the game that way, he's always going to pick up knocks. You've just got to crack on and deal with it."
The injury setback comes hot on the heels of the heavy criticism the flanker received following England's premature exit from the World Cup.
Leaked reports from an enquiry into England's poor showing in New Zealand saw Moody partially blamed for a perceived drinking culture within the camp, although ex-England team manager Martin Johnson was among those to defend Moody's performances both off and on the field.