"Sister Nirmala's life was devoted to service, caring for the poor and underprivileged. Saddened by her demise. May her soul rest in peace," Modi said in a statement.
"My deepest condolences to the Missionaries of Charity family on the passing away of Sister Nirmala," he added.
Sister Nirmala Joshi breathed her last in Kolkata this morning. She was 81.
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.
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.