Sharon Foster, writer of Shoot the Messenger, said it was unreasonable to expect multicultural schools to teach it and that it would be better for black children to learn it from their parents or from supplementary schools.
The film, which will be broadcast on BBC2 next week, has been labelled "the most racist film in the BBC's history" by its opponents. It tells the story of a young black teacher who becomes furious with his own race after he is falsely accused of assaulting a pupil. In one scene he gets angry with fellow guests at a party who suggest more black history should be taught in schools and tells them they should "get over slavery".
Ms Foster has stressed she does not share all the views expressed by the character, played by Spooks actor David Oyelowo. But she told The TES she believed that schools in Britain should not teach special lessons on black history or take part in such initiatives as Black History Month in October.
"I'll probably get into trouble for this, but I think black history is the black community's prerogative," she said. "I don't see how it is something white people can teach. If black parents think their children need it so bad, they should give it to them themselves."
Ms Foster added that it was unreasonable to expect multicultural schools to provide history lessons tailored for every one of their pupils, whose families could come from Asia or Eastern Europe, so black students should not be singled out for special treatment.