The mother Le Thi Hai was not at home when the body was found.
Relatives searched and found Ha near a riverbank in the area. People tried to calm her down as she was in a panic mode and reported to local authorities.
"After hours of investigating, police identified the baby's mother as a suspect. The cause may be postpartum depression," a commune official said.
According to authorities, Hai and her husband had two sons. Their eldest is more than four years old.
Since the birth of the second child, the mother had suffered mentally, often having conflicts with some family members. She had previously threatened to throw the child into a well, but was stopped in time.
On Saturday, Hai was taken to a medical facility for psychological examination.
The investigation team stated after doctors determined her health condition, they would take the mother's testimony to further probe the murder.