Moody sustained the knee injury during Bath's one-sided Heineken Cup victory over Aironi last weekend. He could make his return in the Calcutta Cup match at Twickenham on March 13.
"It is always disappointing to lose a player and leader of Lewis's calibre, but as I have consistently said, good teams adapt to injuries and that is what we intend to do," said England head coach and Lions legend Martin Johnson.
"While this could still mean Lewis plays a role in the tournament, it does mean that another player gets the chance to step up and make it hard for him to get the shirt back."
The injury was worse than first hoped and he joins England teammates Tom Croft and Courtney Lawes on the casualty list.
"It's slightly more frustrating than at first thought," admitted Bath coach Steve Meehan. "We'll of course make sure he receives the best medical attention."
Moody toured New Zealand with the Lions in 2005 making five appearances including two Test matches in which he scored one try.
Johnson is set to name Moody's replacement next Monday, with the likes of Steffon Armitage of London Irish and Northampton Saints pair Tom Wood and Phil Dowson in line to step up from the Saxons.
South African born Leeds Carnegie flanker Hendrie Fourie is now the favourite to wear the No7 shirt having impressed for his adopted country since his making his Test debut in November.
Johnson intends to announce the new England captain in the week leading up to the tournament opener against Wales in Cardiff on Friday, February 4, with Harlequins No8 Nick Easter a strong favourite to be given the armband.
As for Moody himself, the former Leicester star will undertake his rehabilitation at Bath but will keep in regular contact with the England medical team.