The Lumieres Cinema Association said the 68-year-old director had been suffering from a long illness.
Her film Rachida, about a teenage teacher’s struggle against terrorism in Algiers, was her most well-known work.
The movie, which won several prizes all over, took her five years to make and was the first to be directed by a woman in Algeria.
Rachida has been the only Algerian film screened for the Un Certain Regard prize. Bachir was married to fellow Algerian director Mohammed Chouikh. She has a son and three daughters.
During the Black Decade, Bachir-Chouikh stayed in Algeria where she worked as a film editor on her husband’s films.