The 14-year-old girl was said to have copied a crime show by taking 12-month-old Sumit Singh as he played outside his home in India.
A neighbour spotted the teenage girl wrapping him in a cloth and then dropping him into the nearby sewage drain.
Investigating officer Surendra Singh said the girl denied her actions for days claiming she only threw garbage into the drain but eventually confessed to copying a TV show.
Officer Singh said: "She said she did it because she had watched a TV programme in which a woman had thrown a baby in a drain. She said she'd wanted to see if the police could catch her because the police never caught the woman in the programme."
A month on, the baby's body hasn't been found. Santosh Singh, 34, and his wife Urvashi, 29, from Indore, Madhya Pradesh, in central India, are devastated at losing their only child.
Santosh said: "We have to remain hopeful that he's alive. We have to believe he survived the fall and was swept down river. Maybe he's being looked after somewhere."
Police said the teenage girl is now in a juvenile centre until her trial reaches court.
Her family has confirmed she used to sit in front of the TV for hours watching Indian TV programmes such as Savdhaan India, a Hindi-language crime show that focuses on real-life crime stories in India.
"She used to go mad and hit anyone who tried to change the TV channel,'" her father said.