Anita Mazumbar was born on June 24, 1937, in Mussoorie, India. The town, in the Himalayan foothills, served as a resort destination for residents of Delhi. Her father was D.N. Mazumbar, a Bengali businessman. Her mother, Toni Nime, was German, and Anita grew up speaking German at home and Hindi to friends. She learned English as soon as she went to school, so she always associated it with reading and writing. She studied at Queen Mary's School in Delhi and received a bachelor's degree with honors in English literature in 1957 from the University of Delhi. She married Ashvin Desai in 1958.

Desai's novels feature lyrical descriptions of India's landscape, and much of their conflict is derived from the foreigners who feel trapped outside society. Several of her books examine the role of women in Indian society, and many describe family relationships in contemporary life. Her characters struggle with issues of identity after the end of the British colonial period in India and with the role various languages play in their lives as they see Urdu, the language of India's poetry, being supplanted by the more widespread Hindi, and by English, the language of international commerce and modern, Western education.

In Desai's first novel, ‘Cry, the Peacock' (1963), a woman struggles to find her own identity. Her relationship with her older husband seems doomed, and Desai used the relationship to examine traditional Indian marriage and gender relations. ‘Bye-Bye, Blackbird' (1971) explores Indian immigrants living in London and their attempts to integrate their Eastern sensibilities with their Western surroundings. ‘Fire on the Mountain' (1978), which won the Winifred Holtby Award of the Royal Society of Literature, shows generational changes by examining the relationship and differing perspectives of an old woman and her great-granddaughter. The complexity of the novel was compared to 19th-century Russian literature and was praised for its poetic quality. ‘Clear Light of Day' (1980) features a family reunion at which two sisters examine their memories and their history. The novel was widely praised for its literary richness and vividness. The reader was invited into the world of the pre- and postcolonial Indian family. Once affluent, the family lives in a decaying home, and family members recall earlier days. The action in the novel, as in many of Desai's novels, was mostly internal.

Desai's other novels included ‘Voices in the City' (1965); ‘Where Shall We Go This Summer?' (1973); ‘Games at Twilight' (1979); ‘The Village by the Sea' (1983), which won the Guardian prize for children's fiction in 1983 and was made into a motion picture in 1992; ‘In Custody' (1984), which was filmed in 1994; ‘Baumgartner's Bombay' (1988), which won Hadassah Magazine's Hadassah prize in 1989; and ‘Journey to Ithaca' (1995).

Desai was a member of the advisory board for English of the National Academy of Letters in Delhi beginning in 1972. Known in India as the Sahitya Akademi, it awarded Desai its top prize in 1979. Beginning in the 1980s she taught in the United States and in England at colleges including Smith, Mount Holyoke, and Girton College of the University of Cambridge. In 1993, the Massachusetts Institute of Technology made Desai its first professor of writing in more than 20 years. She also wrote short stories that were published in such magazines as Quest, Harper's Bazaar, Thought, and Fesmina. Desai was a Fellow of the Royal Society of Literature and a Member of the American Academy of Arts and Letters.