The England international was withdrawn from the Gunners' starting lineup ahead of their 3-1 victory over Stoke City at the weekend after complaining of abdominal pain.
The 24-year-old was then sent to Germany for an operation, which Wenger has insisted was carried out without any complications.
"Walcott had surgery and it went very well," Wenger told Sky Sports News. "He's coming back [from Germany on] Thursday so it's what we expected there were no complications."
Wenger is hopeful that Walcott will return to fitness ahead of Arsenal's clash against Norwich City on October 19.