The 19-year-old, who made 14 appearances on loan at Bolton last season, has returned to Arsenal for this term with high hopes about challenging for a first-team spot.
Miyaichi had been included in Arsenal's squad for their Far East pre-season tour but only managed to play the first half of Sunday's 2-2 draw with Kitchee in Hong Kong, when he looked far from his best.
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The Japan international also failed to play against Manchester City in Friday's 2-0 loss in Beijing and speaking after Sunday's draw with Kitchee, Wenger told reporters Miyaichi has been battling injury.
"He had an ankle problem and we were not sure to play him. We did not play him against Manchester City because he is not 100 per cent at the moment, physically," Wenger said.
"I think you could see that he is not at his best at the moment. I think he needs two or three more weeks' work to come back to his best."