Malone was born in Monroe County, Alabama in 1942, the fourth of eight children. Her parents both worked at Brookley Air Force Base; her father served in maintenance and her mother worked as a domestic servant. Her parents emphasized the importance of receiving an education and made sure that their children attended college. Each of Malone's older brothers attended Tuskegee University. Her parents were also active in civil rights and often participated in local meetings, donations, and activities in the community that promoted equality and desegregation. As a teenager, Vivian was often involved in community organizations to end racial discrimination and worked closely with local leaders of the movements to work for desegregation in schools.
Malone attended Central High School, where she was a member of the National Honor Society. In February 1961, she enrolled in Alabama Agricultural and Mechanical University, one of the few colleges for black students in the state. She attended Alabama A&M for two years and received a Bachelor's degree in Business Education. Malone had wanted to pursue a degree in accounting, a field of study not offered by Alabama A&M at the time. Moreover, the bachelor's degree Malone received was issued to her before the University had been fully accredited by the Southern Association of Colleges and Schools. To earn an accredited degree in accounting, Malone would have to transfer to another university.