The Greater Gothenburg Fire and Rescue Service said there was no natural cause behind the explosion. The fire service added there was no gas pipeline in the house.
Police said they had opened an investigation but had no suspects at the time.
At least three of those taken to hospital were seriously injured, Goteborgs-Posten, a local paper, reported. The local hospital said three women, all over 60, were seriously injured.
The fire service said 15 units were on the scene. Eleven ambulances were also in attendance.
Emergency services said several hundred people had been evacuated from the vicinity.
“It's awkward. There are at least three stairwells that are affected,” said Lotta Molander of the fire service.
The fire service said it was alerted to the explosion just before 5am. Jessica, a resident of the block, told a local paper she was woken at 4.30am by a loud bang.
She lives in a low-floor flat but says she was unable to exit the building by the stairwell, leaving her to descend from the balcony.
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.
Axel Josefson, the mayor of Gothenburg, said it was a very serious incident due to the location of the block and the number of families affected. “Many Gothenburgers have lost their homes here today,” he said.
Additional reporting by Reuters