In comments published in a 2011 article in The New Indian Express, Pandey shared that her father was a gazette officer with the education department, and that her mother worked with Hindustan Copper. She also revealed that she has one older sister and a younger brother.
Pandey was in class 12 when she entered films, but was advised to pursue her degree before continuing acting. Despite choosing biology with mathematics in class 12, Disha decided to pursue arts to be able to complete her degree more easily. In 2011, she reported that she completed her first year BA in Human Rights.
