The 19-year-old forward picked up the injury in Berlin yesterday during England's training session ahead of their international friendly with Germany.
While commentating on France v Uruguay for French TV channel TF1, Wenger said: "Theo dislocated his shoulder during training, he will be out for at least three months."
Walcott was taken to hospital in agony after suffering the dislocation in a freak accident as he fell in the rain at the Olympic Stadium.
Although Walcott's shoulder was quickly put back into place, the player was in understandable discomfort when he returned to England's team hotel, where an assessment was made over his return to London.
"We are all very disappointed but the important thing is for Theo to travel home and make a quick recovery," England manager Fabio Capello said on Tuesday.
Walcott flew home before England's 2-1 win in Berlin last night.
His injury will only reinforce Wenger's belief that friendly internationals are a dangerous waste of time in mid-season.
Wenger, speaking after his Arsenal side had lost to Aston Villa last weekend, said: "It is particularly not welcome at the moment because it is at a period where you want your players to recover a little bit.
"I don't see what you gain from this friendly because there is no game. You can explain a friendly to prepare for an official match but after this there is no international game for four months."
And, as he digests the news seeping out of the German capital, Wenger will know Arsenal are the ones who will suffer most from Walcott's unfortunate accident.
With eight major stars missing already, the loss of Walcott is just another name added to that list.
Walcott will now miss several key league games, including key visits to Manchester City and Chelsea, with Liverpool due at the Emirates on December 21.
Arsenal's place in the Champions League knock-out phase is by no means secure even though they currently top Group G.
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