The 25-year-old picked up the injury following a challenge he made on Black Cats striker Steven Fletcher and was subsequently stretchered from the field of play.
"I have broken my fibula. Hopefully I can make a speedy recovery," Wilson wrote on Twitter.
|7/1||Stoke City are 7/1 with William Hill to concede three goals to Norwich City|
The Stoke manager has used four natural centre-backs in his defence in the past, however, and could deploy right-sided full-back Andy Wilkinson on the opposite flank as an alternative.