The England winger picked up the problem during the Gunners' 3-0 defeat to league leaders Chelsea on Sunday, after coming on as a half-time substitute.
The hamstring complaint is described by Arsenal as "short term", and Walcott will be desperate to return as soon as possible as he is yet to complete a match this season after shoulder and knee problems.
Wenger also has Alex Song suspended for Stoke's visit to the Emirates Stadium but right-back Bacary Sagna has recovered from his ankle injury.
"We had Sagna out injured but, normally, he will be available," said Wenger. "However, Theo Walcott will not be available. He has a hamstring injury.
"As for the other players we had injured, the long-term ones I do not even speak about. But the players who looked to be shorter - like (Gael) Clichy, (Abou) Diaby and (Nicklas) Bendtner - will not be available. And, of course, Song is suspended for the weekend."
Walcott's absence denies Wenger another option for the central striker role following Robin van Persie's ankle injury, which will rule out the Holland forward for five months.
Eduardo and Carlos Vela shared the duties during the defeat to Chelsea but neither of the strikers impressed.
However at the end of a difficult week, there was at least some solace for the Arsenal manager. Speaking to club's website, he reported positively regarding the condition of Robin van Persie.
"I have not talked to Robin yet but the news I got from the surgery was it went very, very well. There was a lot of disturbance on our side recently (about his injury) but the surgery went well."