The 29-year-old Republic of Ireland international has now undergone surgery to correct the problem which has sidelined him since November last year.
Manager Gus Poyet admitted earlier this month that a lengthy period of rehabilitation would make it unlikely that Westwood would figure for either club or country before the end of the current campaign.
However, the Uruguayan said on Thursday: "He has had the operation. Everything went all right, he is fine, so he starts his recovery next week.
"It's difficult to put a time on it because in the end, it was better than we thought.
"Initially when they went in and they checked, it was not as bad as they thought, so it probably be shorter, but it's difficult to say a time."
Summer signing Vito Mannone has made the most of Westwood's absence, starting the club's last 15 games since taking over from the Irishman during the 1-0 Barclays Premier League defeat at Hull on November 2.
Indeed, such has been the former Arsenal keeper's form for the Black Cats that Manchester United have been credited with an interest in signing him to provide back-up to David de Gea.
Coincidentally, reports of United's interest started to circulate as Sunderland were linked with a move for Millwall's David Forde, the man who has replaced Westwood as the Republic's number one, with former Coventry man's current contract due to expire during the summer.