Detectives are treating the blaze in Dalry, Ayrshire, last night as attempted murder.
The man aged 39 and a 48-year-old woman were in the upstairs flat in Lynn Avenue at around 11.30pm when the fire broke out.
After trying to extinguish it themselves the pair jumped from a window.
The woman was treated for injuries to her arms at Crosshouse Hospital in Kilmarnock where she remains under observation.
The man is in a stable condition in Glasgow Royal Infirmary after suffering superficial burns and smoke inhalation.
Fire crews were able to extinguish the blaze before it spread to other flats.
Detective Inspector Scott McClelland said: "This would appear to have been a targeted attack on the people in the flat, however at this time the motive is not known. The consequences for them, and indeed the others in the block of flats, could have been much worse had the fire taken hold."
Anyone with information is asked to contact police on 101 or Crimestoppers on 0800 555 111.