The former Manchester United man limped off in the early stages of the game with reports suggesting the cause is knee ligament damage.
Black Cats manager Martin O'Neill admitted it would a big blow to the club to lose the defender before the start of the Premier League season.
"Wes is the worry," O'Neill told the Sunderland Echo. "It could be a bad one, but we really don't know at this stage. You're told one thing at half-time and another thing at full-time, so, really, it's too early to tell.
"We'll probably only find out once we're home and it settles down, but hopefully it won't be too bad because he's an important player for us."
New signing Carlos Cuellar also had to come off during the Wearsiders' win but O'Neill revealed that he was withdrawn as a precaution.
Goalkeeper Simon Mignolet and midfielder David Vaughan are also struggling with knocks picked up during their tour of South Korea.
"It's disappointing that he [Cuellar] couldn't get more minutes under his belt, but he felt a tightness in his thigh and did the right thing and came off," O'Neill explained.
"You don’t want to go risking injury in pre-season and Carlos did the smart thing and came off.
"Simon was precautionary for the game. We'll assess him when we get home.
"David Vaughan has had a frustrating time of it. He felt his groin and missed the first match, then had an absolutely excellent training session, only for him to feel it again at the end of it."