The raven-haired beauty plays a young mum whose journalist husband is kidnapped and killed in the upcoming A Mighty Heart, which is based on the true story of Mariane and Daniel Pearl.
Make-up artists apparently darkened the star's skin for her to play the role, a move which has angered campaigners.
They claim the part should have gone to a mixed-race actress.
"I had assumed that the days when white actors took on the roles of black people had long passed away," the Daily Star quotes one protester as saying on a website.
"You can't tell me that Halle Berry or other women of African descent wouldn't have been a better choice," said another.
The movie started shooting in India this week.
It tells the story of Daniel Pearl, who was snatched and beheaded by Islamic terrorists in 2002, and his wife Mariane, who was pregnant when her husband was abducted.
Mariane has said she is thrilled the Tomb Raider star is playing her in the film.
"I'm delighted Angelina Jolie will be playing my role. I deeply admire her work," she said.