The Nigeria international sustained the problem in Saturday's surprise 1-0 Premier League success over Manchester City.
Odemwingie later confirmed on his Twitter account that he requires surgery and will miss most of the 2014-15 season, and Stoke boss Hughes believes the 33-year-old's absence will be felt in more ways than one.
"It's a significant injury and unfortunately it's a long-term one but Peter has a great attitude to work and life in general," Hughes told the club's official website.
"He's always got a smile on his face and he's going to need those qualities. It will be a long road back but we wish him well.
"We'll miss Peter around the place. He'll do his rehab here so we'll see him in the dressing rooms and around the building but we'll really miss him out on the training field where he's a big character.
"But we've got a great medical staff here and they will get him back as soon as it's possible and I'm sure he'll be as good as new."
Odemwingie has unsurprisingly been omitted from Stoke's Premier League squad list, which can be changed during the January transfer window.