"Some TV channels are wrongly reporting that the Chief Minister is no more. This is totally baseless and false," a statement from the hospital said.
"They are advised to rectify this mistake based on this press release."
Apollo said that Jayalalithaa, 68, who suffered a cardiac arrest on Sunday evening, "continues to be on life support at the hospital".
A large number of doctors from Apollo and AIIMS continue to provide all life saving measures, Sangita Reddy, Managing Director of Apollo Hospitals, had tweeted earlier.
But before the clarification came, a Sun TV report that Jayalalithaa was no more triggered frenzy both outside the hospital, where thousands had gathered since Sunday evening, and at the AIADMK headquarters.
A group of emotionally charged AIADMK activists tried to barge into the hospital after breaking the police barricades but were pushed back by the police.
Many others simply broke down, unable to check their emotions. There were loud cries of "Amma, Amma!"
At the AIADMK headquarters in Chennai, the party flag was brought down to half mast. It was restored to its original position once the Apollo statement came.
Inside, hundreds of people wept on hearing the Sun TV report. "How can you leave us?" cried one man.
Apollo has said that Jayalalithaa, who was admitted to the hospital in September, was in very critical condition.