Satyam Yadav, 26, of west Delhi's Nangloi area, was found hanging inside her home around eight a.m., a police officer said.
The body of her one-and-a-half-year old daughter, Vanshika, was lying on the bed.
"It seems Yadav hung herself after strangulating her daughter. But we cannot confirm anything before the postmortem," Police Commissioner V. Renganathan said.
Yadav was a councillor from ward number 43 in Nangloi (East).
She was a native of Bulandshahr in Uttar Pradesh and moved to Delhi in 2010 after her marriage to Pawan Yadav, a teacher in a municipal corporation school.
Satyam's family members have registered a complaint against her in-laws alleging that she was murdered because of dowry.
"Satyam's in-laws were demanding Rs.10 lakh. We went to Delhi to bring her back to Bulandshahr. They refused to let her come and said they will not leave her until their demands were fulfilled," said Satyam's elder brother Nishat Yadav.