Ostriker was born in Brooklyn, New York, on November 11, 1937, to David Suskin and Beatrice Linnick Suskin. Her father was employed by the New York City Department of Parks. Ostriker's mother wrote poetry and read Shakespeare and Browning to her daughter, who soon began writing her own poetry as well as showing an interest in drawing. Initially, Ostriker had hoped to be an artist, and she studied art as a teenager and young adult. Two of her books, Songs (1969) and A Dream of Springtime (1979), feature her own graphics on the covers.

Ostriker received her bachelor's degree in English from Brandeis University in 1959 and her master's and doctorate from the University of Wisconsin. Her dissertation became her first critical book, Vision and Verse in William Blake (1965); later, she edited and annotated Blake's complete poems for Penguin Press. In 1965, Ostriker began teaching at Rutgers University.