The body of local hairdresser Margaret Evans was discovered in a house in Knockancor Drive in Portstewart on Wednesday afternoon.
The woman, who was in her 60s, and a well-known businesswoman in the town where she run a hairdressing salon..
A PSNI spokesman said detectives were still investigating the circumstances surrounding the woman’s death.
A post mortem is due to be carried out today to determine the cause of the death.
The man can be held for up to 24 hours but detectives can apply to a court for an extension to his detention to question him further.