Moody was due to make his first appearance of the season in Saturday's Premiership clash against Wasps.
But the Tigers convened an internal disciplinary hearing on Wednesday night after Leeds officials cited Moody for an incident during last Monday's A League game between Leicester and Leeds.
Tigers' suspension means that Moody is sidelined until October 6, although he still faces a Rugby Football Union hearing in Coventry on September 20.
Moody will miss Premiership appointments with Wasps, Bath and Leeds, plus a Powergen Cup tie against Welsh regional side the Dragons.
He only appeared as a second-half substitute against Tykes' A team, scoring one of Leicester's eight tries as they triumphed 53-22.
The RFU disciplinary panel, chaired by Richard Moon, will inevitably take Moody's club ban into account when considering the case later this month, but they could also impose their own period of suspension.
Moody's place in the Leicester starting line-up on Saturday will be taken by Brett Deacon.
"Obviously, we would have liked to have had Lewis available, but Brett's had a superb pre-season and he is a more than capable replacement," said Tigers forwards coach Richard Cockerill.