Shots were fired near a youth shelter in the city center, a police spokesman told the German news agency DPA.
Five people - four women and one man - died at the scene of the shooting, German police said. A sixth person later died in hospital.
Several others were injured, some seriously, DPA reports.
In addition to the suspected shooter, police are investigating two other people suspected of possible involvement.
The motive is not clear.
The town of Stade in the German state of Lower Saxony has a population of around 48,000 and is located a few kilometres west of Hamburg.
According to police, there is no further threat to the public.
Germany has some of Europe's strictest gun laws, requiring anyone under 25 to undergo a psychiatric examination before applying for a gun licence, AFP reports. Mass shootings are relatively rare.
