Police said they had opened an investigation. The Sahlgrenska University Hospital spokesperson said three women were seriously injured among the people taken to hospital, Reuters reported.
Emergency services said they were working to evacuate people and put out fires in the building.
"Several apartments and stairwells are affected. It is at present unclear what has caused the explosion," the emergency services for the wider Gothenburg area said.
A spokesperson for the emergency services said that several hundred people had been evacuated from the vicinity of the explosion and fire.
The immediate cause of the explosion and fire was unclear. The Nordic country has contended with surging gang crime in recent years, with rival groups employing explosives and fire arms to settle scores.