A man fired a shot at a moving car in Delmenhorst, seriously injuring the 35-year-old driver in the head.
Also in the woman's car were three children, ages eight, ten and twelve.
According to the first findings, they remained unharmed and are being psychologically cared for, as the Delmenhorst police announced on Friday evening.
According to the investigations so far, the police assume that the woman was targeted.
However, the background is still completely unclear.
"We're investigating in all directions," said a police spokeswoman.
The alleged perpetrator initially escaped, but was caught a little later.
A police spokesman said at the scene that a man had been arrested.
The 41-year-old is an urgent suspect and has connections to the woman's family.
Officers are investigating an attempted homicide.
According to the police investigation, the allegedly dark-clad perpetrator rode a bicycle towards the woman's moving car.
He then fired a shot, the police spokeswoman said.
Crime scene footage showed the driver's door window shattered.
The woman went to a clinic.
The police could not provide any information on the exact severity of the injury early Friday evening.
First of all, a traffic accident in the street in downtown Delmenhorst, not far from the train station, was reported to the officials on Friday afternoon.
The woman's car drove into a bollard on the side of the road after the crime.
Rescue workers then found that the woman had been shot in the head, the police spokeswoman said.
ktz/dpa