Police say the gunman acted alone and is thought to be dead. It is unclear if the attacker is among the six or seven fatalities reported by German media.
As yet, “there is no reliable information on the motive”, police say.
A number of people were also injured in the shooting on Deelböge street, Gross Borstel district, late on Thursday.
Police say they found a dead person at the scene who they believe may have been a perpetrator and investigations are continuing.
They were called at about 21:15 local time (20:15 GMT) on Thursday to reports that shots had been fired in the building, police spokesman Holger Vehren said.
Officers who went in found people who “may have been seriously injured by firearms, some of them fatally”, he said.
“The officers also heard a shot from the upper part of the building and went upstairs, where they also found a person. So far we have no indications that any perpetrators fled.”
He said police had not yet identified the victims and work at the crime scene continued.
“All we know is that several people have died here, several people have been injured, they have been taken to hospitals,” Mr Vehren said.
