Byatt was born in Sheffield as Antonia Susan Drabble, the eldest child of John Drabble, QC, and Kathleen Bloor, a scholar of Browning. Her sisters are the novelist Margaret Drabble and the art historian Helen Langdon. Her brother Richard Drabble QC is a barrister. As a result of the bombing of Sheffield during the Second World War the family moved to York.
Byatt's upbringing was fairly unhappy as she struggled against her domineering mother. She was educated at two independent boarding schools, Sheffield High School and the Quaker Mount School in York. She noted in an interview in 2009, "I am not a Quaker, of course, because I'm anti-Christian and the Quakers are a form of Christianity but their religion is wonderful – you simply sat in silence and listened to the nature of things."
She did not enjoy boarding school, citing her need to be alone and her difficulty in making friends. She went on to Newnham College, Cambridge, Bryn Mawr College in the United States, and Somerville College, Oxford. Byatt lectured in the Department of Extra-Mural Studies of the University of London (1962–71), the Central School of Art and Design and from 1972 to 1983 at University College London.
She married Ian Charles Rayner Byatt in 1959 and had a daughter, as well as a son who was killed in a car accident at the age of 11. The marriage was dissolved in 1969. She has two daughters with her second husband Peter John Duffy.
Byatt's relationship with her sister Margaret Drabble has sometimes been strained due to the presence of autobiographical elements in both their writing. While their relationship is no longer especially close and they do not read each other's books, Drabble describes the situation as "normal sibling rivalry" and Byatt says it has been "terribly overstated by gossip columnists" and that the sisters "always have liked each other on the bottom line."