Police were called to the property in Glenure Loan, Edinburgh, at around 12.30am today.
When officers arrived, they found the body of a 47-year-old man. A 37-year-old woman was detained at the scene and the death is being treated as suspicious, police said.
Part of the street was closed off while forensic officers examined the scene.
A force spokesman said: "Local residents will be aware that an area of Glenure Loan has been cordoned off as forensic examinations are ongoing. I would like to reassure local people, however, that there is no risk to nearby residents or the general public.
"Investigations are at an early stage and anyone who has any information which could assist with our investigation is asked to call Police Scotland on 101 or provide the information anonymously through Crimestoppers on 0800 555 111."