The victims are yet to be identified, and work at the crime scene continues.
Police say they found a dead person at the scene who they believe may have been the perpetrator.
They were called at about 21:15 local time (20:15 GMT) on Thursday, to reports that shots had been fired in the building on Deelböge street, Gross Borstel district, 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.