P Anbukodi, 32, committed the crime in Namakkal on Monday night.
When she and her husband went to a private hospital in Salem on Monday to treat her child, she was told how much the treatment would cost -- about Rs 5,000 a day.
Realizing she cannot afford the treatment, a depressed Ms Anbukodi committed suicide after killing her son on Monday night, the police said. The fire service retrieved the bodies on Tuesday.
An outbreak of dengue has claimed 27 lives this year in Tamil Nadu.