Sister Nirmala had replaced Blessed Teresa of Calcutta as head of the charity she founded, Missionaries of Charity in 1997.
During her time leading the organisation the nun expanded its operations to 134 countries including Afghanistan, Israel and Thailand.
She had been suffering from a heart condition and her health had recently deteriorated, according to local media.
Archbishop of Kolkata Thomas D'Souza told AFP: "She had been suffering from a heart disease for quite some time, but she never lost her smile and was always cheerful.
"She passed away peacefully, surrounded by sisters praying for her.
"Sister Nirmala carried forward Mother Teresa's legacy of compassion, gentleness, service to the poorest of the poor and holiness of life.
"Even after she ceased to be head of Missionaries of Charity, she served the people with the same zeal as she did before."
The nun's body is now in a church near to where she lived ahead of her funeral tomorrow.
Indian Prime Minister Narendra Modi led tributes on Twitter.
Sister Nirmala's life was devoted to service, caring for the poor & underprivileged. Saddened by her demise. May her soul rest in peace.
— Narendra Modi (@narendramodi) June 23, 2015