The 20-year-old Miyaichi played 45 minutes in a 3-1 win over Nagoya Grampus on Monday and another 45 minutes in beating Urawa Red Diamonds 2-1. Wenger signed up Nagoya native Miyaichi in January 2011 and immediately loaned him to Feyenoord.
Miyaichi was later loaned to Bolton Wanderers in January 2012 and to Wigan Athletic in August 2012. He returned to action in March after being sidelined for four months with to a right foot injury.
"He's done well tonight, he was sharp and better than the other night already. He's in the team. I like his play," said Wenger.
"I believe that he is in a position now where he needs to play, to have a good chance to compete at the top level. At the moment he stays in the squad. If we should buy more players, I have to reassess the situation. At the moment, he stays with us," he added.
Arsenal also thrashed Indonesia Dream Team 7-0 and Vietnam's national side 7-1 before coming to Japan.