Police say the shooting was carried out by a lone gunman who may be among the dead, although this has yet to be officially confirmed, Sky news reported.
Shots were fired at the Jehovah's Witnesses' Kingdom Hall in the Gross Borstel district, with police alerted at 9.03pm on Thursday.
Police said the gunman opened fire after entering the building, before allegedly fleeing to the first floor. Officers arriving on the scene then heard a shot from an upper floor and found a body upstairs.
Police spokesperson Holger Vehren said none of the officers fired their weapons.
One witness told reporters, "We heard shots. "There were 12 continuous shots. Then we saw how people were taken away in black bags."
In a statement posted on Twitter, Hamburg Police said: "We found a lifeless person in a community centre in #GroßBorstel who we believe could be a perpetrator.
"In order to rule out the involvement of other perpetrators, we carry out checks and search extensively."
The motive for the attack is currently unclear.
Police added that a large operation was under way in the next-door Alsterdorf district, in the northern part of the city. The area is a few kilometres north of the downtown area of Hamburg, which is Germany's second-biggest city.
A number of armed officers were pictured near the scene alongside dozens of police cars.
MNA/PR
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