Satish Kumar and Madasamy were taken into custody with an intent to create panic among the public following a complaint from the ruling AIADMK party’s IT Secretary.
The police have registered 43 cases on charges of spreading rumours about Jayalalithaa’s health.
The 68-year-old Chief Minister was hospitalized on September 22 for fever and dehydration.
The doctors later said she needed a longer stay at the hospital as she was suffering from infection and put her on respiratory support.
The police recently registered a case against a resident of France, also on charges of spreading rumours.
Meanwhile, leaders of political parties continue to visit Apollo Hospital to enquire about Jayalalithaa’s health.
Congress leader M. Krishnaswamy told the media later that AIADMK leaders had told him that Jayalalithaa’s condition was improving.