Rai, 83, is survived by a son and three daughters.
A former principal of a local girls college, Rai was an active member of BJP women's wing.
She was Lt Governor of Puducherry from April 1998 to July 2002.
Rai was accorded a state funeral as her body wrapped in tri-colour was taken to a local crematorium.
District Collector Saurabh Rao, Commissioner of Police, K K Pathak, SP Nagpur rural Dr Manoj Sharma and city Mayor Anil Sole were present at the funeral.