"If a poor woman desires to look beautiful, we will support her financially," state health minister C Vijayabaskar told AFP.
"Whether they require medical procedures or beauty treatment, it will be free."
Tamil Nadu is ranked among the top states in India's public healthcare system, compared with ailing government-run facilities in many other parts of the country.
But critics of the new scheme said the state government is wasting public money on cosmetic surgery instead of spending it on treating serious ailments.
Cosmetic breast surgery is becoming increasingly popular in India, but private hospitals charge anywhere between $2,300 and $3,800 for the procedure.
More than 90,000 such procedures were carried out in the country in 2016, according to the International Society of Aesthetic Plastic Surgery, up from 50,600 in 2010.
V Ramadevi, who heads the clinic, told AFP some women want such surgery because they "face psychological issues that may severely impact their lives".
"Their career, (their) marriage are derailed because they are taunted and their confidence is shattered," she said, adding that the clinic expects up to 150 women a month to take up the offer.
Tamil Nadu has for decades offered freebies to its marginalised population, mostly under the government of popular actor-turned-politician Jayalalithaa. She died in 2016 but her party still rules the state.