The Japanese international joined the Latics from Arsenal in a temporary deal at the start of the campaign and has already featured in four matches.
"He is only 19 but his performances against Fulham and West Ham show he's someone who is ready to have a massive, massive impact this season," Martinez told reporters.
"I was very pleased with his performance. Overall his contribution was very, very good and he is a player that is growing."
Miyaichi spent last season on loan at Bolton Wanderers but couldn't help the Trotters secure their Premier League survival.