Police were called to the incident at 9.10am.
“A child in the family rang and said that her mother had been shot,” said Christer Harplinger, a spokesman at Halland police.
The weapon was found by police but no details have been released.
Both the man and the woman were resident at the same address. The woman was aged around 40 and the man, who was previously known to the police, is aged around 55.
Several children were in the apartment at the time of the shooting. They have now been taken into care by the social services.