The chief minister of Tamil Nadu state suffered a heart attack on Sunday night and died at 23:30 local time (18:00 GMT) on Monday, Chennai's Apollo Hospital said.
Thousands of her supporters had gathered to pray for her recovery.
Extra police have been deployed in the southern state amid fears of unrest among her supporters.
The former film star served as Tamil Nadu chief minister four times. She had been receiving treatment for months.
Jayalalitha is revered by many but seen by her critics as having created a cult of personality over the years.
(Last Updated at 7.41pm Dec. 05)
India's Jayaram Jayalalitha still 'critical' after heart attack
One of India's most popular and powerful politicians, J Jayalalitha, remains in a critical condition after suffering a heart attack on Sunday night, the hospital treating her said.
Thousands of people are standing vigil outside the hospital in Chennai.
Ms Jayalalitha, 68, has been receiving treatment for months and was last seen in public in September.
The former film star has been Tamil Nadu chief minister four times and is revered by many in the state.
With the extreme devotion she inspires among her supporters, many of whom refer to her as "Amma" (mother), there are concerns that a serious deterioration in her condition could spark unrest.
Police have been put on alert across Tamil Nadu and outside her official residence in Chennai (Madras).
There have already been scuffles outside the hospital, following incorrect reports of her death in Indian media. The reports have since been retracted, and a flag flying at half-mast over her party's headquarters has been hoisted once more.
News of her health over the last few months has been closely monitored and guarded, and in a sign of the sensitivity around the issue two people were arrested for spreading rumours about her health in October.
The latest statement from the Apollo Hospital added that Ms Jayalalitha was being "closely monitored by a team of experts" and she was still on life support systems.
On Sunday evening, the hospital had asked the public to "pray for her speedy recovery".
Leaders, including President Pranab Mukherjee have tweeted, expressing concern about her health.
Last month a letter released by her party seemed to hint at a recovery for the politician saying she had been "reborn" thanks to prayers from her supporters.
As it also urged people to vote for her party at upcoming by-elections, critics said it could have also been an attempt to quell fears about the extent of her illness and mobilise her supporters.