The former Sunderland man had to leave the pitch during Tuesday night's Carling Cup clash, which Stoke won on penalties.
A scan has revealed that there is only minor damage to the hamstring and he could return for the game against Fulham on October 15.
Before then, the Potters play Manchester United, Besiktas and Swansea before heading into the international break.
Despite competing for a place with Cameron Jerome, Peter Crouch and Jon Walters, Jones has played in nine of Stoke's 11 games this season and scored against Norwich in August.
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."
Source: Team Talk
Source: Team Talk