Atlanta police spokesman Eric Schwartz said he believed the victims were all related. A seventh person in the house was uninjured.
The gunman was identified as Abdulaziz Ibrahim, 52.
The shooting occurred around daybreak, Schwartz said.
Inside the house, police found the bodies of Hana Yusuf, 26, and a person named Luna, no last name given, Schwartz said.
A fourth person, Mohmmed Ibrahim, 26, died at Grady Memorial Hospital.
Two others are hospitalized. Police said 3-year-old Amir Addulhakim was in critical but stable condition and Yusuf Ibrahim, 27, was in stable condition.
All the victims are believed to be related somehow. Neighbors told a local radio station that the family was from Ethiopia.