The Deadpool star, 34, said he did not know the race of Major Ben Daimio when he accepted the part in the comic book adaptation.
He said he was stepping down “so the role can be cast appropriately”.
The initial casting prompted accusations of Hollywood “whitewashing” following other recent rows.
Skrein noted in a statement posted to his 34,000 Twitter followers that there had been “intense conversation and understandable upset” since he was cast in the film as the Japanese-American character.
“It is clear that representing this character in a culturally accurate way holds significance for people, and that to neglect this responsibility would continue a worrying tendency to obscure ethnic minority stories and voices in the arts,” he said.
The move won immediate praise from many on social media, including from people who were not previously fans.
“Thank you for doing this. You just gained a follower and I’ll definitely check out the next thing you work on,” one person said.