Wilson injured his left leg as he made a challenge on Black Cats striker Steven Fletcher just a few minutes into the second half and the Republic of Ireland international had to be carried off on a stretcher.
Potters boss Tony Pulis said in his post-match press conference that Wilson had been taken straight to hospital.
And writing on his Twitter account, the player later said: "Have broke my fibula. Hopefully I can make a speedy recovery
"Thanks every1 for the support. Really appreciate it."
Stoke this morning confirmed the news on their official website, with Pulis saying: "Marc will be out for a while, but we are not sure at this stage for how long."
Thanks again every1 for the support. Really appreciate it. Have broke my fibula. Hopefully I can make a speedy recovery.