The incident occurred in the early hours of Wednesday in the town in Warangal Urban district, about 200 km from Hyderabad.
Police said the accused abducted the child sleeping with her parents on the terrace of her house in Kumarpalli area of the town. When the couple did not find the child on the bed, they raised an alarm.
Some people in a nearby lane found a youth running away after dumping the child on the ground. They chased, caught hold of the accused, identified as 28-year-old Praveen, and handed him over to police.
The baby, who was bleeding, was shifted to a hospital where she was declared brought dead. Police sent the body for autopsy.
The incident sent shock wave across the town as people launched spontaneous protests, demanding that the youth be hanged in front of them for the heinous act.
Men, women including youth and students came together to stage protests. They formed a human chain and refused to call off the protest till the guilty is hanged publicly. Tension prevailed as police rushed there to forcibly end the protest. Some protestors were taken in custody.
Panchayat Raj Minister E. Dayakar Rao, who belongs to the same district, said the incident had shocked the entire society. He directed the police to take immediate stringent action against the accused.
( With inputs from IANS )