It was suspected that the parents might have poured some inflammable liquid on the children and set them ablaze before committing suicide in a similar manner.
Mounting debts was believed to the reason for the family taking the extreme step, police said.
Residents of an apartment complex in Neelankarai here alerted police and fire services personnel after they noticed thick smoke billowing out of a house.
The personnel found the charred bodies of K Venkatesan (42), his wife Malarvizhi (37) and Harini (7) in the house.
"The child was gasping and was in a serious condition when admitted," a senior doctor of the KMC said.
Preliminary inquiries revealed that Venkatesan had incurred heavy debts and did not go for work for some time.