Wilson, who has scored five league goals so far this season, more than half his team's total, was carried off on a stretcher in the first half after attempting to play on following a strong challenge by Stoke's Philipp Wollscheid.
"It doesn't look good at this moment in time," Bournmeouth boss Eddie Howe told the club's website.
"He's in a brace and on crutches. He's in a bit of pain and there's a bit of swelling there.
"We won't know until we get it scanned and properly looked at, but it's worrying for us. It looks like it could be another serious knee injury.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"He wanted to carry on and stay on, such is his nature. The physios were aware of there could be a potential injury there and they relayed their concerns to him."
Bournemouth have already suffered long-term injuries to Max Gradel and Tyrone Mings.
"You wouldn't wish any serious injury on any footballer, but to get three in one team, to key players as well, is mystifying really," Howe said.
Defeat left top-flight debutants Bournemouth 15th.
(Reporting by Martyn Herman; editing by Toby Davis)
