Hacham Nissim Abraham Ashkenazi was born to Rachel and Raphael in Izmir, Turkey. He learned Torah from his father and from the sages of Izmir of his time.
Hacham Nissim Abraham Ashkenazi married Rachel Sharuta. Despite her 18 pregnancies, none of their children survived past early childhood.
Hacham Nissim Abraham Ashkenazi officiated as dayan in the Izmir rabbinic court alongside Hacham Haim Palagi. His home was a meeting place for scholars and his door open to the city's needy residents.
Hacham Nissim Abraham Ashkenazi passed away on 15 Elul 5620 (1860). He was a prolific writer, and while only some of his work was published during his lifetime, his brother's children had several of his books printed. Among his books one counts Nechmad LeMar'eh – a commentary on the Jerusalem Talmud, Ma'aseh Abraham – responsa on the four parts of the Shulchan 'Aruch, Darash Abraham – sermons and commentary on the Torah, Na'eh Doresh – a collection of sermons, and Na'eh LeHodot – a commentary on the Book of Psalms.