The first police patrol to reach the scene at around 7am on Monday morning met the man in the stairwell of the apartment block.
The man, aged about 25, was taken to the police station where officers decided to submit him to a psychiatric examination, said Anders Kristiansson of Malmö Police.
It is not yet known how the woman was murdered or what her connection was to the man.
Lars Mahler, spokesman for police in Skåne, said that she had “a close relationship” with the man.
Police forensic experts were on Monday morning examining the apartment and interviewing neighbours.