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.
