Jones hobbled off in the first half of Tuesday night's Carling Cup clash against Tottenham, which Stoke won on penalties.
A scan on his hamstring has revealed that there is only minor damage, but he is set to miss the matches against Manchester United, Besiktas and Swansea before potentially returning after the international break against Fulham on October 15.
Assistant manager Dave Kemp told the club's official website: "There is a slight problem, but it's nothing too serious.
"Kenwyne will miss this weekend's game and more than likely next week's two games as well, but after that we have the break which will give him a bit of time to get up and running again.
"It is disappointing for us, and for him, because he has carried on from the end of last season with his form and done very well for us.
"He looked extremely bright against Tottenham before he had to come off."