The stand-in captain had to be substituted in the closing minutes of Saturday's game against Livingston, where it was thought he had dislocated a shoulder.
However, tests have today shown that nothing is dislocated or broken, but ligament damage has been done.
The news comes as a massive dissapointment to Martin O'Neill, as McNamara has been one of Celtic's best performers this season.
O'Neill has also told that he will be keeping "a close eye" on defender Bobo Balde, who suffered a knee in his back, also late on in the game.