O'Connor was born in Glenageary in County Dublin and was named after Sinéad de Valera, wife of Irish President Éamon de Valera and mother of the doctor presiding over the delivery, and Saint Bernadette of Lourdes. She is the third of five children, sister to novelist Joseph, Eimear, John, and Eoin.
Her parents are Sean O'Connor, a structural engineer later turned barrister and chairperson of the Divorce Action Group, and Marie O'Connor. In 1979 O'Connor left her mother and went to live with her father and his new wife. At the age of 15, her shoplifting and truancy led to her being placed for eighteen months in a Magdalene Asylum, the Grianán Training Centre run by the Order of Our Lady of Charity. In some ways, she thrived there, especially in the development of her writing and music, but she also chafed under the imposed conformity. Unruly students there were sometimes sent to sleep in the adjoining nursing home, an experience of which she later commented, "I have never - and probably will never - experience such panic and terror and agony over anything."