A file on the matter is being prepared by gardaí for the DPP.
The woman has been named as 38-year-old Siobhán Kearney.
It is understood a post-mortem examination revealed the mother of one may have been strangled.
A murder investigation was immediately launched by gardaí.
“Gardaí from Dundrum Garda Station, Dublin, have launched a murder investigation following the discovery of a woman’s body in a house at Knocknashee, Goatstown on Tuesday morning last,” said a garda spokesman.
It’s believed a relative of Ms Kearney found her body in an upstairs bedroom in the family home on Carne Road, Knocknashee.
The emergency services were contacted but she was pronounced dead at the scene.
When gardaí arrived at the house, the cause of death was not clear.
A preliminary post-mortem examination was conducted at the scene.
A garda spokesman said the woman’s body was removed to Dublin City Morgue, where a full post mortem was carried out by State Pathologist Dr Marie Cassidy.
“The gardaí are not releasing details of the post mortem for operational reasons,” he said.
However, it is understood that the examination revealed that Ms Kearney was strangled. The injuries may have been inflicted at some point on Monday or possibly early on Tuesday.
Details of the murder only emerged yesterday after it became clear that the death was not natural or suicide but an unlawful killing.
The man was arrested at about 7am yesterday morning at a different address in connection with her death. He was detained at Dundrum Garda Station under the provisions of Section 4 of the Criminal Justice Act, 1984 until yesterday evening.
It’s understood Ms Kearney had only recently returned from Spain, where she ran a hotel business. She is survived by her husband and her three-year-old son.
She was a sister of Sunday Independent journalist Brigid McLaughlin.