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Williams picked up the problem during Wales' 19 v 13 victory over Ireland last weekend but was able to finish the game.
However after an injury assessment on Sunday he was sent for a scan and the results revealed ligament damage, which means the victory over Ireland is likely to be his last appearance in the tournament.
"Shane will be out of action for a period of six to eight weeks after sustaining damage to the posterior cruciate ligament in his left knee during the match at the weekend," said Wales' medical manager Prav Mathema.
Wales coach Warren Gatland has already added Scarlets wing George North to his squad in advance of the trip to Stade de France and there are no further call-ups expected.
