Miyaichi scored a penalty in a 3-1 friendly win against the Gunners manager's former side Nagoya Grampus.
The 20-year-old, who signed for Arsenal two years ago, has been recovering from an injury picked up in March but was included for the Asia Tour and Monday's match in Japan.
Olivier Giroud had opened the scoring, his sixth goal of the Asia tour, before usual penalty taker Mikel Arteta gave Miyaichi the chance to score from the spot to make it 2-0. Theo Walcott added a third before Kisho Yano got one back in front of a crowd of almost 43,000.
Speaking about the penalty, Wenger told the club's website: "It was not planned. When Ryo scored I thought it was a good decision from Arteta.
"Ryo was not completely fit to play but it was a special occasion that I did not want him to miss. He just needs to come back to full fitness and then the rest will come along.
"I like his pace, his mobility and his movement off the ball. I like players who can move when others have the ball. There is also his attitude, commitment and desire. That is why I decided to keep him."