The victim, hailing from Thimava Royanakupppam took the extreme step owing to poverty, they said.
The woman pushed her two male children, aged 3 and 2 before jumping into the farm well in the village this morning.
Villagers retrieved the bodies of the children from the well and rescued the woman and admitted her to Kurinjipadi government hospital, they added.
A case has been registered and investigation is on, police said.