Tolstaya was born in Leningrad into a family of writers. Her paternal grandfather, Aleksei Nikolaevich Tolstoy, was a pioneering science fiction writer, and the son of Count Nikolay Alexandrovich Tolstoy (1849–1900) and Alexandra Leontievna Turgeneva (1854–1906), a relative of Decembrist Nikolay Turgenev and the writer Ivan Turgenev. Tolstaya's paternal grandmother was the poet Natalia Krandievskaya. Mikhail Lozinsky (1886-1955), her maternal grandfather, was a literary translator renowned for his translation of Dante's "The Divine Comedy". Tolstaya's sister, Natalia was a writer as well. Her son, Artemy Lebedev, is the founder-owner of Art. Lebedev Studio, a Russian web design firm.