The woman noticed the blaze when she woke up at around 5.30 AM at her house in Kakaravada village of the district.
While trying to rescue her young son, the woman, Jayalakshmi (23), suffered severe burns and died on the spot, police said.
Later, a fire tender from Gudivada rushed to the spot and managed to control the flames.
The child, Harsha, also suffered burns and was rushed to Vijayawada Government hospital where he succumbed, police said.
A case has been registered, police said, adding that short-circuit was suspected to be the cause of the fire even as a probe was on.