Walcott, who returned to make two brief substitute appearances in November after nearly a year out with a serious knee injury, hurt his thigh while on international duty.
"He has an injection today so he will not play. Galatasaray (in the Champions League) is also too early," Wenger told a news conference on Friday.
Left back Nacho Monreal will also miss the game after picking up a knock in the 1-0 win against Southampton in midweek but keeper Wojciech Szczesny is available again after returning to training.
Arsenal have a poor record at Stoke, winning only once in the league at the Britania Stadium since the Midlands club returned to the top flight in 2008, but Wenger played down the significance of what is a notoriously tricky fixture.
Relations between the clubs were soured when Arsenal's Aaron Ramsey suffered a broken leg in a tackle by Ryan Shawcross in 2010.
"It's always a tough and committed place to go but we dictate the way we want to play at that level of commitment," Wenger said. "It's a football game, not a hate game. We want to focus on playing football.
"Stoke don't lose many games at home and have good records against many good teams"
(Reporting by Martyn Herman; Editing by John O'Brien)
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