Police and emergency services arrived at the intersection of John Ericssons gata and Falkmansgatan after receiving a call shortly after 8pm about what was believed to be a dead woman sitting in car.
Witnesses reported hearing "pops" in the area and police were able to confirm upon arrival that the woman had lost her life.
"She has likely died from gunshot wounds," Skåne police spokesperson Nils Norling told the TT news agency.
However, he refused to say how many shots had been fired.
Police have classified the incident as murder or with an alternative charge of manslaughter.
The car was found at an intersection located near Pildammsparken and police cordoned off much of the area as they launched their investigation into the killing.
Forensic specialists began combing the scene on Sunday night and weapon-sniffing dogs were also brought it as a part of the investigation.
However, the search failed to turn up a weapon or any shell casings.
While the woman's identity has yet to be confirmed, police suspect it is the 39-year-old woman who is the registered owner of the vehicle in which she was found.
Shortly before 2am on Monday a 44-year-old man was detained on suspicion of murder.
"At the moment, it looks like it was some sort of family drama," duty officer Martin Carlsson of the Skåne police told TT.
The man later admitted to having caused the woman's death.
"He has confessed to having shot the 39-year-old woman," said Börje Aronsson of the local police to TT on Monday afternoon.