The Arsenal and England forward complained of abdominal pain in the final warm-up before the victory over Stoke at the Britannia Stadium before being withdrawn from the starting line-up.
The club decided to send Walcott abroad for an operation and Wenger told Sky Sports News: "Walcott had surgery and it went very well. He's coming back (from Germany) Thursday so it's what we expected there were no complications."
Walcott will be unavailable for England's closing Group H qualifiers against Poland and Montenegro - a Wembley double-header which will determine whether Roy Hodgson's side qualify automatically for Brazil.
Walcott started both England's September qualifiers, a 4-0 win against Moldova and a goalless draw in Ukraine.