Mirza was born in India. Her father, Frank Handrich, was a German graphics and industrial fair designer, architect, artist and interior designer based in Munich. Her mother, Deepa, is a Bengali who is an interior designer, landscaper and currently does social work as a volunteer to help alcoholics and drug addicts. When Dia was four-and-a-half years old, her parents got divorced. Afterwards, her mother married Ahmed Mirza, a Dakhini Muslim man from Hyderabad, and Dia (then only a toddler) was given the last name of her step-father. Dia's step-father died in 2003.