The car was found in Tierp, near Uppsala, on Sunday. A dead body was found inside the car and another outside.
"The person found outside the car is a man," Christer Nordström of the Uppsala police confirmed to the TT news agency.
Police said that the blaze was not related to a traffic accident, but added that they do not suspect any crime.
The bodies have been sent for forensic examinations, where they are hoped to be identified.
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On Monday morning the Upsala Nya Tidning (UNT) reported that the deceased were likely a couple who were in their early eighties. The car, which was found on a deserted road near the woods, was registered to the man.