The 29-year-old Republic of Ireland international has been sidelined for several weeks by the problem, which requires an operation to correct.
However, a scheduled appointment has had to be cancelled because Westwood has been ill and is taking a course of anti-biotics, and that delay means his season could effectively be over.
Black Cats boss Gus Poyet said: "It has been postponed because of a little illness. You cannot have an operation when you are ill, so he is on antibiotics now."
Asked how long the player is likely to be out, the Uruguayan said: "I would like to say three to four months. Now, if you are going to think when is the season going to finish, it's probably to the end, yes."