Fire crews were called to the blaze, in the second floor flat at Rowan House on Bishport Avenue, in Hartcliffe at about 12:00 BST on Monday.
An Avon and Somerset Police spokesman said they were treating the death of the man, who was in his 40s, as "unexplained".
He said the force was continuing its inquiries on behalf of the coroner's office.
A man has died in a fire at a block of flats in Bristol.