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.