Sister Nirmala took over leadership of the charity organisation in 1997.
A Missionaries of Charity official said Sister Nirmala was not keeping well for the past few days and her health was gradually deteriorating.
Her body would be brought to Mother House tomorrow morning and the funeral will be held at 4 PM.
"Any one who wants to pay respect can come to Mother House tomorrow", the official said.
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West Bengal Chief Minister Mamata Banerjee paid her tributes on the microblogging site, Twitter, saying Kolkata and the world would miss Sister Nirmala.
Sister Nirmala was born to a Brahmin soldier who came from Nepal in Ranchi on July 23, 1934. She had joined the Order at the age of 17.
On March 13, 1997, six months before Mother Teresa's death, Sister Nirmala was selected the Superior General of the Missionaries of Charity.
Sister Mary Prema was elected to succeed Sister Nirmala during a general chapter held in Calcutta in April 2009.