She said he will always be remembered as a "crusader of humanity, religion and spirituality".
His death is a huge loss and he leaves behind a rich legacy, the Congress president said.
"Country and humanity has lost a saint in the death of Swami and he led a selfless life in the service of humanity and built temples in India and abroad to spread Indian culture and spirituality," she said.
Congress vice-president Rahul Gandhi also paid tributes to the head BAPS Pramukh Swami Maharaj.
"Deeply saddened by the passing away of HH Pramukh Swami Maharaj. His message of compassion & service will remain an inspiration," the Congress vice president said on Twitter.
Pramukh Swami, who was ailing for some time due to old age-related problems, breathed his last at 6 PM in Sarangpur in Gujarat's Botad district. He was 95.