Shauneille Perry was born on July 26, 1929, in Chicago, Illinois to a prominent African-American family. She is the daughter of Graham T. Perry (1894–1960), one of the first African-American assistant attorneys-general for the State of Illinois and his wife, the former (Laura) Pearl Gant (1903–1957), one of the first African-American court reporters in Chicago. She is the niece by marriage of real-estate broker and political activist Carl Augustus Hansberry (who married her father's sister, Nannie Louise Perry) and his brother, Africanist scholar William Leo Hansberry. She is also the first cousin of playwright Lorraine Hansberry, Carl Hansberry's daughter.