The two have been accused of posting false news on social media websites about the condition of Jayaram Jayalalitha, chief minister of Tamil Nadu state, who has been in hospital since last month.
‘The accused were arrested on Monday for posting false news on Facebook. We are taking these acts seriously,’ Senthil Kumar, head of the serious crimes branch in the state capital Chennai, told AFP, without elaborating on the content of the posts.
Forty-three similar cases have been filed against unknown persons and a hunt launched to arrest them, Kumar said.
Jayalalitha was admitted to hospital in Chennai on September 22, and tens of thousands of her supporters are anxiously awaiting news about her health.
Authorities have provided few updates on her condition, initially saying the 68-year-old leader was suffering from fever and dehydration.
On October 3 the hospital said she was on respiratory support and a critical care expert was flown in from Britain.
Scores of her followers gather outside the hospital every day, praying in unusual ways for her recovery.
Jayalalitha, a former movie star known as ‘amma’ or mother, has a cult following in one of the country's most prosperous states. She is serving as chief minister for the third time after winning elections this year.
Police fear rumours could provoke her supporters to turn violent or even engage in self-harm.
Last week one of her supporters was injured after setting himself on fire, while an elderly man suspended himself from a crane with steel hooks pierced through his skin.
Pictures showed scores of children with metal arrows piercing their cheeks holding Jayalalitha's picture as they prayed for her recovery.
Local opposition parties have demanded in vain that the government issue regular health bulletins. A few individuals have approached the courts on the matter.
Jayalalitha is one of India's most powerful women politicians but her career lasting more than three decades has been marred by corruption charges. She was jailed briefly on two occasions, most recently in 2014.
But she has repeatedly sprung back to power, mostly with the help of vast election-time giveaways that ranged from laptops to bicycles and kitchen appliances.