Bhanupriya was born in Rangampeta village, near Rajamundry, Andhra Pradesh, into a Telugu family. Her family settled in Chennai, Tamil Nadu. She has a younger sister Shantipriya who was also a film actress in 1990s.
Bhanupriya fell in love with Adarsh Kaushal, a Hyderabadi settled in the United States as a digital graphics’ engineer. Subsequently, the couple got married at the Sri Venkateswara temple in Malibu, California on 14 June 1998. The couple have a daughter Abhinaya born in 2003. Bhanupriya divorced Kaushal in 2005 and returned to India, where she resumed her acting career. Bhanupriya now lives in Chennai with her daughter Abhinaya.