In 1971, Ozick received the Edward Lewis Wallant Award for her short story collection, The Pagan Rabbi and Other Stories. In 1997, she received the Diamonstein-Spielvogel Award for the Art of the Essay for Fame and Folly. Three of her stories won first prize in the O. Henry competition. In 1986, she was selected as the first winner of the Rea Award for the Short Story. In 2000, she won the National Book Critics Circle Award for Quarrel & Quandary. Her novel Heir to the Glimmering World (2004) (published as The Bear Boy in the United Kingdom) won high literary praise. Ozick was on the shortlist for the 2005 Man Booker International Prize, and in 2008 she was awarded the PEN/Nabokov Award and the PEN/Malamud Award, which was established by Bernard Malamud’s family to honor excellence in the art of the short story. Her novel Foreign Bodies was shortlisted for the Orange Prize (2012) and the Jewish Quarterly-Wingate Prize (2013).
David Foster Wallace called Ozick one of the greatest living American writers. She has been described as "the Athena of America’s literary pantheon," the "Emily Dickinson of the Bronx," and "one of the most accomplished and graceful literary stylists of her time."