Her body, draped in the Indian flag, is on display at a large public hall.
Prime Minister Narendra Modi was among those who visited to pay tribute.
Extra police have been deployed in the state amid fears of unrest.
The extreme devotion she inspires among her supporters, many of whom refer to her as "Amma" (mother) have led to concerns that they could resort to self-harm or violence.
Earlier reports of her death, which were swiftly withdrawn, prompted scuffles between police and her supporters outside the private hospital.
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