The facility targeted in the northern town of Stade includes temporary accommodation for pregnant women and young mothers with children
Two people were arrested, including the suspected shooter.
Other people were wounded, police said, but they did not give a figure.
Police said the shooting took place in the facility on Dankersstrasse, a street south of the town centre. That facility includes temporary accommodation for pregnant women or young mothers with children.
There was no danger to the public, police said. Video footage after the shooting showed a large police presence, along with other emergency service personnel and several ambulances.
Two suspects were arrested, one of whom is believed to have fired the shots. Police said they were working to establish the background to the shooting and what exactly happened.
