Police apprehended the man after the child’s mother raised the alarm at 5am on Saturday.
The father is suspected of strangling his daughter. Repeated attempts by ambulance personnel to resuscitate the child were unsuccessful, local newspaper Göteborgs-Posten reports.
The child’s mother was taken to hospital but is not believed to have sustained any physical injuries.
Police sealed off the couple’s home on Saturday morning as forensic experts conducted an examination at the scene on Sweden’s third largest island, which has a population of 15,000.