Emergency services were called to Cobbinshaw House South in Calder Gardens, Edinburgh, just after 2pm on Thursday to a report that a man had fallen from a block of flats.
The 35-year-old was taken to hospital, where he died a short time later.
Police are treating the death as unexplained.
A 32-year-old man has been arrested in connection with the incident which happened in the Wester Hailes area of the city.
A police spokesman said: “The death is currently being treated as unexplained and a report will be submitted to the procurator fiscal. Inquiries remain ongoing.”