The man had recently had his prison sentence reduced, allowing him to take regular furloughs.
Around 11am on Saturday, a woman was found stabbed to death in an apartment on Kungsholmen in central Stockholm.
The 36-year-old was arrested the same day, and later charged with murder.
The man was already serving a life sentence for another murder committed 13 years ago, reports the Expressen newspaper.
The then 23-year-old man had assaulted and stabbed an intoxicated 46-year-old man to death in Storfors in Värmland in central Sweden.
In May, Örebro district court converted the man's life sentence to a period of 21 years based on the man's good behaviour and the court's assessment that there was little risk he would commit further crimes.
Head prosecutor Gunnar Brodin, who made the recommendation that the court reduce the man's sentence, does not want to take responsibility for the decision.
“I was going on the recommendations of the National Board of Forensic Medicine (Rättsmedicinalverket) and the Swedish Prison and Probation Service (Kriminalvården). He has been well-behaved and has been granted regular furloughs for several years,” Brodin told the TT news agency.
Brodin explained that the risk of reoffence was low, but that in hindsight it appears granting the 36-year-old furloughs was "a poor decision".
The murdered woman has not yet been identified and her relatives have not been informed, according to police.
Nor has the suspect been questioned by police.
"He has not admitted anything but has requested a change of attorney. We have therefore been unable to question him," Stockholm police spokesperson Petra Sjölander told TT.