The winger, 33, needs knee surgery and faces a long spell on the sidelines after picking up the problem in Saturday’s 1-0 win at Manchester City.
He will have the operation in the next fortnight.
“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,” Stoke manager, Mark Hughes, told the club’s 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.”
The former West Brom forward scored five goals in 15 Premier League appearances for the Potters last season after joining from Cardiff in January.
The club won seven of the 15 matches he played, compared to nine of 29 without him.