The crime took place at around 7pm in the city of 100,000 inhabitants in Lower Saxony. The man reportedly drove a white Volkswagen car in front of the two women, got out and opened fire.
The 30-year-old was killed in the gunfire, while her 32-year-old companion was also hit by a bullet and had to be operated on in hospital.
A police spokesperson said on Tuesday morning that “she is no longer in a life threatening situation.”
Police say that they know the name of the gunman, a 38-year-old male, but have not yet identified his whereabouts. Checkpoints have been set up on the autobahn as part of the search effort.
Police have not made any comment as to the relationship between the man and the murdered woman.
Local news site regionalsalzgitter.de reports based on conversations with relatives that the gunman was her former partner, with whom she had four children.
According to the report, the couple had been involved in a legal dispute over access to the children.