Firefighters received a call around 6.30am and when emergency personnel arrived on the scene, the apartment was in flames and filled with smoke.
The man and woman were taken to Kärn hospital in Skövde, but their lives could not be saved.
“We’ve launched an investigation into negligence constituting a public danger,” said Fredrik Sjöstedt of the Skövde police to the TT news agency.
“However, there are no signs that the fire was set intentionally.”
As firefighters fought the blaze, apartments in two nearby entryways were evacuated.
“The others who live there have been allowed to return to their apartments,” said Sjöstedt.