The unidentified child was sleeping in a bedroom at home with his mother and grandmother Thursday, and "when the baby screamed the grandmother discovered what had happened and called for help," Menaming Village chief Firdaus Daulay said.
The news website Okezone wrote the baby's head was severely bitten.
The child was taken to a community health center and later transferred to the Pasir Pangariaian hospital, where he died, the Jakarta Globe reported Friday.
After the incident, the monkey was hunted and killed by village residents, the newspaper added.
LGBT community has 'bullied the American people': Bachmann
Attkisson leaves CBS News, reportedly over network's 'liberal bias'