Saroj Kumari was living with her daughter, Veena Singh, in Noida for over two years.
Former Madhya Pradesh chief minister Arjun Singh's wife died early on Wednesday due a heart attack.
Saroj Kumari, 84, died in her sleep and suffered cardiac arrest, doctors who checked on her in the morning told the family.
Saroj Kumari was admitted at the AIIMS for six weeks and had only returned home on April 25. She will be cremated at her hometown Churhat in Madhya Pradesh, the family said.
Saroj Kumari was living with her daughter, Veena Singh, in Noida for over two years.
Veena Singh said Saroj Kumari's two sons were arriving in Delhi and would take the body to their hometown later in the day after embalming.