The fatal shots were fired late on Christmas Eve when a 57-year-old man was found wounded outside a student residence in the city. He was rushed to hospital but succumbed to his injuries.
A man was arrested close to the crime scene shortly afterwards. He was questioned on Boxing day on grounds of probable cause and was later detained on suspicion of either committing murder or manslaughter.
"We have some idea of what happened but no real clear picture yet," said Tony Pallon of the Skåne police to Sydsvenskan newspaper.
Following the shooting, police combed the scene for evidence and found a gun that was located close to the victim. The suspect's apartment was also examined
Local newspaper Sydsvenskan reported that the victim and the accused were both employed by the University of Lund. The fatal shooting took place in the student neighbourhood of Kämnärsrätten, which was near deserted as most students had gone home for Christmas.
Police said they have interviewed more than a dozen witnesses and intend to submit a full investigation to the prosecutor on Friday.
"This is a deep tragedy," said University of Lund head Per Eriksson to local media.