Williams saw a specialist on Christmas Eve after the problem he picked up in Italy playing in a Heineken Cup match against Treviso earlier this month failed to improve with rest.
He was given a cortisone injection to speed up his recovery and is now hoping to return in mid-January - only weeks before Wales launch the defence of their Six Nations crown.
"The problem is affecting one of the rotator cuff tendons in his right shoulder. Shane had a week off after the Treviso game to rest but the shoulder did not respond," said an Ospreys spokesman.
"He was reviewed by a specialist and had an injection to try to help his symptoms in the short term. Now it's just a case of waiting to see how things go."
Williams missed last weekend's derby win over the Scarlets and has already been scratched from the Ospreys team to face Cardiff Blues at the Arms Park on Wednesday.
Now worried Ospreys bosses have given their star wing another fortnight's rest before finalising a date for a possible comeback in January.
"Shane is definitely out of the New Year's Eve game and has been given two weeks off to rest. He is targeting either the game against Munster or Perpignan in January for his return," added the club spokesman.