Her maternal grandfather, a lawyer by profession, was a friend of Filippo Turati, the prominent socialist writer. Ginzburg's parents were Jewish and Catholic in name only since both were nonbelievers. At the age of three Ginzburg moved from Palermo to Turin when her father was appointed to the chair of anatomy at the university.
Fearing that Natalia would catch a disease in the public schools, which he distrusted, her father had her tutored at home for the duration of her primary education. Later he relented and allowed Ginzburg to attend the prestigious Liceo Alfieri, where she completed her secondary education. In 1935 she enrolled in the Faculty of Letters at the University of Turin but did not stay to complete her studies. She wrote poetry, imitating such writers as Giovanni Pascoli, Guido Gozzano, and Sergio Corazzini, and devoted considerable time to what she called "il mestiere di scrivere" (the craft of writing). She also read voraciously, including French and Russian authors, especially Marcel Proust and Anton Chekhov. She admired two women writers, the American poet Emily Dickinson and the English novelist Ivy Compton-Burnett.
