Shoot The Messenger follows a black computer programmer who quits his job to teach underachieving black children, but is assaulted by one of his pupils and is ostracised by his community.
Ligali, a group which campaigns against misrepresentation of African people in the media, has called it a "flagship programme for racism" and is calling for the programme to be pulled. It is due for broadcast on 30 August.
"This is one of the most racist, demeaning and misrepresentative films ever broadcast and commissioned by the BBC," said Toyin Agbetu, the founder of Ligali.
The film's director Ngozi Onwurah has hit back at the criticisms, claiming the drama simply represents real life, rather than misrepresenting black people.
"Part of the role of a writer is having to look at some of the more uncomfortable things in the world that you know," she told the BBC News website.