The blaze broke out in the three-storey building in Barr Street, Ardrossan, at about 8pm yesterday.
Two fire crews were sent to tackle what was described as a “well-developed fire”.
Police said a 53-year-old man was found in one of the flats and pronounced dead at the scene.
It was the second serious fire in the west of Scotland on Monday evening.
Three adults and two children were taken to hospital following a blaze at a block of flats in Charles Street, Glasgow, at around 5pm.
Twenty other people were checked over by paramedics at the scene but did not need hospital treatment.
The Scottish Ambulance Service said one adult was taken to Glasgow Royal Infirmary while two were taken to Queen Elizabeth University Hospital.
The two children were taken to the Royal Hospital for Children Glasgow.
All five were suffering from smoke inhalation.