According to Norbotten County police, the woman's body showed signs of having been subject to violence.
The scene of the fire, a house just west of Haparanda, has been cordoned off by police and a forensic investigation is underway.
Police were alerted about the woman's body by emergency crews who had arrived to put out the fire, which was first reported at around 6pm Thursday evening.
"When emergency crews pulled the woman out of the burning house and were about to try to recusitate her, they saw that she had injuries which indicated she had subject to extreme violence. I can't say exactly what types of injuries," police spokesperson Anders Calderäng told the TT news agency.
Police are now working to ascertain the woman's identity.
"Police are on the scene speaking with neighbours and anyone who may have seen or heard something. We're also going to carry out our own forensic investigation of the fire-damaged house as quickly as possible," said Calderäng.
While the house was heavily damaged in the fire, it didn't burn to the ground entirely.
"There were flames on the first floor and there was a lot of smoke," emergency crew member Bengt Lindgren told the Expressen newspaper.
Police suspect the fire was set in order to cover up the murder and by late Thursday evening they had identified a suspect.
"We're issuing a nationwide alert for the suspected perpetrator," Erik Kummu of the Norbotten County police told the Aftonbladet newspaper.
As of early Friday morning, an arrest warrant had been issued for the suspect, but police released few other details about the case, adding they will have more to say during a press conference scheduled for later on Friday.