Police Scotland officers said the death of the man shortly after midnight on Christmas Day is being treated as suspicious.
Officers were called to the property in Glenure Loan at about 12.30am.
When they arrived, they found the body of the 47-year-old man.
A 37-year-old woman was detained at the scene. Part of the street in the Clermiston area of the city was closed off while forensic officers examined the scene. Officers also interviewed neighbours as part of the probe.
A Police Scotland spokesman made an appeal for information.
He 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."