She was 82.
Sinha, who was a member of former Prime Minister I K Gujral's cabinet, died at Syracuse in New York, USA. She is survived by three daughters and four grandsons.
"She was suffering from age-related problems and passed away peacefully in her sleep at the home of her eldest daughter, who is a doctor in Syracuse, New York. She will be cremated there on Saturday and her last remains will be brought to Patna after that," said Gayatri Sharma, another daughter of Sinha and a former journalist.
Born in Dhaka (now in Bangladesh) on September 30, 1932, Sinha, a grandniece of Jan Sangh founder Shyama Prasad Mukherjee, received education at Calcutta and Patna Universities.
She got married to freedom fighter and Bihar minister Late Basawan Singh, a native of Vaishali district.
Sinha was initiated into politics by her husband. She was several times elected the national president of Hind Mazdoor Sabha of the socialists and was imprisoned under Maintenance of Internal Security Act (MISA) during the socialist movement of 1974 led by Jaya Prakash Narayan.