Both victims, found dead before 9 a.m. Wednesday, had been fatally stabbed, police told the Aftonbladet newspaper.
Police caught the suspect, identified by the TT news agency as the son of the murdered man, on Wednesday.
The suspect had been sentenced to a psychiatric facility after being convicted of the 1996 murder of his mother, The Local reported.
The Local did not identify the suspect, say where he was held or for how long.
Since his release, he has been repeatedly convicted of theft and was most recently released from jail New Year's Eve, the reports said. He has had no permanent address since then.
Aftonbladet said there was no known motive for the killings Wednesday.
Minutes of the trial in the 1996 murder of his mother stated the man had a "strained" relationship with his father and was often extremely aggressive.
A few weeks before his mother's death, he had called her and said he would "hack her to death," The Local said.
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]
Exploding whale video goes viral on Internet