"He's admitted to the facts of the case, that he shot the 39-year-old woman dead," Börje Aronsson, of the Malmö police told the TT news agency.
The woman's lifeless body was found in a car by police and emergency crews at the intersection of John Ericssons gata and Falkmansgatan shortly after 8pm on Sunday night after witnesses reported hearing "pops" in the area.
According to the Sydsvenskan newspaper, the 44-year-old fled the scene and drove south after firing the fatal shots but turned himself in to police in Trelleborg several hours later.
But even before the man had turned himself in, police had focused their suspicions on the 44-year-old after running the victim's identity through police records and discovering evidence that the 39-year-old had been subject to previous violence from the man.
In addition to one reported case of assault, the 44-year-old had also been slapped with a restraining order.
The killing has parallels with another recent murder of a 39-year-old woman who was stabbed to death by her ex-boyfriend in Malmö in February.
Both cases involve angry ex-boyfriends who were unable to accept that their relationships with the victims had ended, according to Sydsvenskan.
"We've now had three such murders in southwestern Skåne in a very short time, if you count what happened in Landskrona. It's extremely regrettable," Aronsson told the newspaper, referencing the killing in late April of a 19-year-old woman who was stabbed to death, allegedly by her 16-year-old brother because she "brought shame on the family".
Prosecutors are currently putting together a request to have the 44-year-old held on remand on suspicion of murder.