The 25-year-old woman was wandering on the Höhenstraße near the Vienna Woods on Tuesday when a police car passed her. She waved it down and told them she had killed her son.
After hearing her confession police searched her apartment in Favoriten and discovered the body of a child lying under a blanket.
According to police spokesman Paul Eidenberger the body had "superficial injuries" and there was clear signs of "foul play".
The woman told police she had killed her son a few days ago. She then checked into a bed and breakfast and took some medication.
Police have ordered an autopsy of the child's body and the woman will be questioned by detectives on Wednesday.
At present it's unclear what the woman's motive was or if she is suffering from mental health issues, although Eidenberger said she was in a "confused" state.
Police have also questioned the child's father, who does not live with the 25-year-old woman. He told police that they had not had a good relationship and that the woman suffered from depression.
Neighbours told police that the couple frequently quarrelled.