"It's completely unfathomable. We had no idea,” the man’s family told the Aftonbladet newspaper.
The man, who was on the run from police after the kidnapping, was discovered on Monday around 3.30am by Swedish police at a car park in Växjö, southern Sweden.
His clothes were covered in blood and he was asleep, together with his child, in the car.
The 45-year-old man was immediately arrested and he confessed to murdering the missing woman, and was able to point out where police would find the body.
The body of the woman was found in an abandoned cottage by the Grønkjaer ski facility, not far from the man’s house in Norway.
The 45-year-old man, who underwent continued police interrogation in Sweden on Tuesday, is now suspected of murder.
Police have not disclosed any details about the cause of the woman’s death, but Norwegian police said a forensic investigation is underway.
The motive behind the murder also remains unclear, although an Aftonbladet source has pointed to a child-custody dispute.
The 11-month-old boy has been handed over to social authorities, and it remains unclear of who will take care of him in the future.
The 26-year-old woman had reported the man in the summer for harassment.
Norwegian authorities are expected to request his extradition to Norway.