Eight other people were wounded, including a seven-months pregnant woman who lost her unborn daughter, police and prosecutors said at a news conference.
Authorities identified the gunmman only as Philipp F. The 35-year-old, a German citizen and former Jehovah's Witness, began shooting through a window at the hall, where dozens of people were gathered, before entering.
Following the previous shootings, Germany introduced stricter gun ownership rules and the government has announced plans to tighten controls further.
Jehovah's Witnesses are an international Christian denomination that was founded in the United States in around 1870.
The officials said about 50 people were at an event held in the Jehovah's Witness Kingdom Hall in the Alsterdorf district of the city when the shooting started.