Golodryga was born to a working-class family of Bessarabian Jews in Căușeni, Moldavian Soviet Socialist Republic (now independent Moldova), the only child of Zhanna and Vitaly Golodryga. In 1980, when she was 18 months old, her family left the Soviet Union as political refugees, each with $75. They settled in Houston, Texas. She has returned to Moldova only once since then, visiting her grandparents and cousins in 1988. That same year, her grandmother joined them in Houston. Her mother is the Chief information officer of Hess Corporation and her father, a mechanical Engineer, was a consultant for DuPont.