Le'Equipe reported Anelka, who has started both of France's games, insulted Coach Raymond Domenech at half-time, the BBC said. The report did not give details of the alleged insult.
The report said the 31-year-old Chelsea star missed training Saturday.
French Football Federation president Jean-Pierre Escalettes asked Anelka to apologize but he refused. The FFF said in a statement, "Faced by the refusal of the player to publicly apologize, (Escalettes) took the decision in total agreement with the coach and the official members of the delegation present to exclude Nicolas Anelka from the squad."
France captain Patrice Evra was present with Escalettes at the France training camp in South Africa when the decision was taken, the FFF said.
With or without Anelka, France's hope of qualifying from Group A is out of the team's hands after its 0-0 draw to Uruguay and defeat by Mexico. The BBC said France will be eliminated if Mexico and Uruguay draw in their final match.