The woman, identified as A Archana, hanged herself from a ceiling fan apparently after poisoning her 18-month-old daughter A Bhavana and another daughter who is only three-months-old, police inspector PVVN Rao said.
Archana's husband A Sateesh Kalyan Chakravarthi is working in a real estate firm.
"Archana has been living in the flat along with her husband and in-laws. She bolted the door from inside at around 11 AM when her husband went out to work. Her in-laws were also not present in the flat," Rao said.
"He found Archana hanging from the fan while both his daughters were lying dead on floor with froth oozing out of their mouths," Rao said.
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The bodies were shifted to King George Hospital for postmortem.
Rao said Archana was a native of Karnataka and had been married for two years.
"We are yet to find the motive behind the incident," he said.