Harishchandra Yadav, 35, was arrested on Wednesday night, they said.
During interrogation, Yadav said he had committed the crime on Monday when he was drunk, police said.
However, the victim's relatives refused to believe the police and staged demonstrations at Ambedkar Circle here to demand that the "real culprit" be nabbed.
The child's body had been recovered from a drain in Nandola area, two kilometres away from her home.
Irate over the incident, locals had yesterday staged a protest by keeping victim's body on the Baran-Shahbad road.
However, they were later pacified by officials after which her body was sent for postmortem.