She is survived by a son and three daughters, family sources said.
Vidya (84) was elected to the Parliament as a Congress candidate from Vijayawada constituency in 1980 and in 1989.
In 1980, she defeated former Union Minister Dr K L Rao by over one lakh votes in what was then a sensation.
She was the daughter of atheist movement leader Goparaju Ramachandra Rao (GoRa).
GoRa established the Atheist Centre in Vijayawada and his entire family was involved in social service through the Centre.
Vidya won the Jamnalal Bajaj Award in recognition of her services to women.
Meanwhile, Andhra Pradesh Chief Minister N Chandrababu Naidu expressed grief over the former MP's death.
"Vidya rendered exemplary services as an MP. Her work for women empowerment, in particular, was commendable," the Chief Minister said in a statement.
He extended sympathies to the bereaved family.
Vijayawada MP Kesineni Srinivas (Nani), MLA Gadde Ramamohan and others visited Atheist Centre and paid homage to Vidya.