Emergency services were called to the blaze in Seaton Terrace, Irvine, North Ayrshire, at about 2am today.
A 49-year-old woman who was in the house was treated for smoke inhalation by paramedics and taken to Crosshouse Hospital, where she is said to be in a stable condition.
Following initial inquiries, police are treating the incident as wilful fire raising and attempted murder.
Officers want to speak to a man who was seen in the area around the time of the fire.
Detective Sergeant Ian Ross said: "We are carrying out extensive inquiries including door-to-door inquiries to trace the person responsible and discover the motive for the fire.
"I would like to appeal to a man who was described as wearing dark clothing who was seen in the area around the time of the fire to get in touch as he may have information which can help our inquiry.
"I would also appeal to anyone who was in the area last night and saw anything suspicious or anyone hanging around to contact me."
Anyone with information can contact police on the non-emergency 101 number or anonymously via Crimestoppers on 0800 555 111.