The Brazilian national's body was discovered at an apartment on Liberty Street at around 6:30am.
A man in his 20s was arrested by Gardaí and is being at questioned at the Bridewell Garda Station.
A post mortem was carried out on the body of the 28 year old this afternoon by Assistant State Pathologist Dr Margaret Bolster- Gardaí say the results of the exam are not being released for operational reasons.
Garda Press told RedFM News that the investigation is being led by a Senior Investigating Officer and that a Garda Family Liaison Officer has been appointed to liaise with the woman's family.
The scene remains sealed off tonight for a full technical exam and Gardaí say investigations are ongoing.
Bruna Fonseca worked as a contract cleaner at the Mercy University Hospital and in a statement, the hospital said management and staff "are saddened and shocked" at her death.
Management at the hospital say she was a "hard and diligent worker and an esteemed colleague".
Management also extended their deepest condolences to her family and friends in Brazil and her friends in Cork.
