The operation was carried out by the same surgeon who operated on Walcott in 2007.
The winger had been due to play in England's friendly against Germany in Berlin, a match that Fabio Capello's team won 2-1.
Walcott has been a regular for the Gunners this season and, having seen his team collect just four points from their last four league games, Wenger must do without one of his most potent attacking players.
Last season the Derby midfielder Stephen Pearson was ruled out for a month after suffering the same injury.
But Walcott is not expected to return until 2009 - ruling him out of the remainder of Arsenal's Champions League group campaign as well as at least seven Premier League games.
"During Tuesday's training session Theo Walcott dislocated his right shoulder after falling on the pitch," said an FA statement.
"Arsenal's medical staff were advised of the injury soon after the incident."
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