Local councillor Carsten Brokelmann said that the city operates a daycare facility and a primary school in the immediate vicinity of where the shooting happened.
“We are relieved that our staff and the children in the daycare center and elementary school are all safe and well, and I would like to thank the police officers for their service in this chaotic situation,” he said in a statement.
“At the same time, our deepest sympathies go out to the victims of this terrible act and their families,” Brokelmann said.
The police has warned that unverified information about the incident has appeared online and asked people not to spread any rumours as this could hinder the investigation.
Stade, some 45 kilometres (27 miles) west from Hamburg, is a historical town of about 50,000 people