Wilson fell awkwardly as he challenged Steven Fletcher just a few minutes into the second half and the Republic of Ireland international had to be carried off on a stretcher.
Pulis had initially been hoping that Wilson's injury was not serious, but he is now waiting to learn how long the player will be out of action.
Stoke manager Tony Pulis said: "Marc will be out for a while, but we are not sure at this stage for how long."
The player added: "Have broke my fibula. Hopefully I can make a speedy recovery. Thanks for the support, I really appreciate it."
Meanwhile, Pulis was left to bemoan Stoke's luck after they failed to find the breakthrough against the Black Cats.
He added: "If you have a look at the game on a whole we did have the better opportunities and the best chances and you need a break.
"You need one to drop for you. If we'd have scored one then it's a different game."