The woman was arrested yesterday from the village in Dhar, around four hours from state capital Bhopal.
No one else was present when the woman allegedly killed her baby with a sickle.
Neighbours heard the child falling silent abruptly and a little later, saw the woman locking up and leaving without her child. She allegedly went to a relative's house.
"The child was crying for milk and the mother was working in the kitchen. She got irritated and lost her temper. She took the sickle and struck her, killing her instantly," said police officer CB Singh.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.