The woman, named only as Elizabeth, is in hospital and police hope to question her on Monday.
On Sunday, the local priest Thomas Adamu dedicated his prayers to nine-year-old Paul. There were tears among the congregation of 70. Mayor Josef Mayrhauser said that everyone knew the family, and no would have thought that Elizabeth was capable of such an act of violence.
A neighbour, Anni Neubacher, told the Krone newspaper that single-mother Elizabeth was known to have mental health problems and had been treated for burnout and had taken time off from her job due to exhaustion.
Police say that Elizabeth killed her son on Saturday, by severing an artery in his arm with a kitchen knife while he slept. She then tried to kill herself in the bathroom, but her mother found her at noon, still conscious. It's not clear what her motive was, and no suicide note was found in her house.