Alicia Suskin Ostriker was born Alicia Suskin in Brooklyn, New York, to David Suskin and Beatrice Linnick Suskin. Both parents held degrees in English from Brooklyn College. Her father worked as a playground director for the New York City Department of Parks, and her mother tutored students in English and math, and later taught folk dancing. Her mother wrote poetry and read William Shakespeare and Robert Browning to her two daughters, Alicia, and a younger sister, Amy David, born in 1948.
Ostriker received a B.A. from Brandeis University in 1955, and in 1958, she married the astronomer Jeremiah P. Ostriker, with whom she had three children: Rebecca (1963), Eve (1965), and Gabriel (1970). She earned her M.A. (1961) and her Ph.D. (1964) from the University of Wisconsin. In 1965, she began to teach in the Rutgers University English Department, where she became a full professor.