The 15-year-old girl, a local resident, has confessed to strangulate the child to death, police said.
"The two-year-old girl was missing from her home since June 10. Based on the complaint made in this regard, we conducted inquiry into the matter leading to apprehension of the juvenile.
"During interrogation, she confessed that mother of the deceased had quarrelled with her five days before the incident and to avenge the insult, she killed the child," police said.
According to police, on finding the two-year-old playing alone on June 10, the accused took her home and "immediately" strangulated the child to death.
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"Three days after the incident, we received information regarding recovery of the child's body in a plastic bag. We immediately rushed to the spot and found the body of the child whose neck was wrapped with a cloth," police said.
Police further said that taking into account gravity and sensitivity of the case, a team of Special Task Force under the Operation Cell of East District along with the team of PS-Kalyan Puri was formed to probe the case.
Police said sustained interrogation of the 15-year-old was carried out in presence of lady police according to guidelines issued by Juvenile Act. Initially she tried to mislead cops to get benefit of her young age, but confessed to the crime later, police said.