The police arrested a 33-year-old woman from Herne in the Ruhr area.
She is said to have intentionally killed her two children in 2011 and 2012.
The boys were then 2 and 19 months old, said a police spokesman on Wednesday.
In 2018, the woman is said to have physically abused a third child, also a boy who was just over two years old at the time.
The public prosecutor's office in Bochum and a specially formed investigative team managed to gain so much knowledge that a pre-trial arrest warrant was issued for two murders, among other things.
The arrest warrant was therefore executed on Tuesday by members of the investigation team.
Since then, the 33-year-old has been in custody.
The public prosecutor's office and the police want to give details at noon in Bochum.
him/dpa