The child was discharged yesterday after being treated at a hospital but her condition worsened and she died last night at her house, they said.
Meanwhile, three persons were admitted to the Ramanathapuram Government hospital with dengue symptoms.
Deputy Director of Health Uma Maheswari said anti-dengue operations were on full swing in the district following detection of cases. Public have been advised to drink boiled water and to prevent water stagnation around their houses to prevent breeding of mosquitoes, main carriers of the virus, she added.
Tirunelveli District is the worst hit in the southern districts accounting for nearly 30 deaths caused by the fever.
A central team of doctors and experts had last week visited Tirunelveli to take stock of the situation and discussed steps being taken by the state officials.