The body of a 25-year-old woman was discovered in the family's apartment at 9.15 am on Monday morning after police received calls from concerned neighbours.
The brother of the dead woman called the police at 9.39 am and reportedly confessed to the killing. He was arrested and remains in custody.
Forensic teams entered the property, on the town's seafront, and removed the body at 11.45 am.
Police sources said that the woman had died "violently", according to Spanish daily Diario Sur which described the killing as a 'beheading'.
Some Spanish media have reported that the man is of Ecuadorian origin.