Officers and an ambulance were called out to the apartment block in Norsborg, southern Stockholm just after 2am on Thursday when they were told a woman had fallen from a third floor balcony.
A 30-year-old man was arrested at the scene, initially suspected of attempted murder but later changed to murder after the woman died.
It is not yet certain what relationship the man may have had with the woman and police are working to clarify the details around the incident.
“The circumstances are unclear, but there is reason to assume that a crime has been committed,” Stockholm police spokesperson Sven-Erik Olsson told news agency TT.
A forensic investigation of the apartment is due to take place on Thursday.