The emergency services were called to Coombe Street, Exeter at 1700 BST on Sunday.
The body of a 47-year-old man was discovered in the flat at Turnworth Court.
The man's next of kin has been informed. Police are treating the death as unexplained.
Latest on the fatal fire story, plus more Devon and Cornwall news
Police are investigating the death of a man following a fire at a block of flats.