Davis was born on August 11, 1965, in St. Matthews, South Carolina, the daughter of Mary Alice (née Logan) and Dan Davis. She was born on her grandmother's farm in the Singleton Plantation. Her father was a horse trainer, and her mother was a maid, factory worker and homemaker. Two months after she was born, her family moved to Central Falls, Rhode Island, with Davis and two of her sisters, leaving her older sister and brother with her grandparents.
Her mother was also an activist during the civil rights movement. At the age of two, Davis was taken to jail with her mother after she was arrested during a civil rights protest. She has described herself as having "lived in abject poverty and dysfunction" during her childhood, recalling living in "rat-infested and condemned" apartments. Davis is a second cousin of actor Mike Colter, known for portraying the Marvel Comics character Luke Cage.