One of the men died at the scene, the other died later at the Sahlgrenska University Hospital, a hospital spokesman told news agency TT.
Two people are reported to have left the apartment shortly after shooting the men.
“The strange thing is that we only received one call about this,” said the duty police officer at Gothenburg police.
“Only one neighbour called. You would think that the whole building would hear when something like this happened, but this was not the case,” he said.
TT reported that it had spoken with witnesses who said at least two people left the scene after the shooting.
“There was a third too, but I believe that he lives in this building,” said a witness who saw events from his home. He said that one of the men disappeared down a staircase between two of the apartment blocks, and onto Bredfjällsgatan.
The man who raised the alarm said he was woken by the sound of screaming and fighting. He also heard bangs, but wasn’t sure that it was the sound of a gun firing. He looked out his window and saw a man disappear from the building.
“He was wearing a white mask,” the witness said.
Shortly afterwards another man left the building. Police were informed at 1.44 am. Seven police cars were sent to the scene. Police dogs were deployed in search of the men, but without result.