A woman, a 17-year-old boy and two girls, aged 16 and 11, were taken to hospital after after they escaped from the blaze at a house in Heckmondwike, near Huddersfield, West Yorkshire, at about 4.13am on Sunday.
The 17-year-old is in a serious but stable condition, suffering from burns and injuries caused by jumping from an upstairs window, West Yorkshire Police said.
Paramedics treated the woman and two girls for smoke inhalation at the scene before they were taken to hospital.
Police said all the house occupants escaped through upstairs windows.
Detective Superintendent Mark Swift, of West Yorkshire Police Homicide and Major Enquiry Team (HMET), said: "This is clearly a very serious incident in which a male has suffered burn injuries and three females have also suffered smoke inhalation.
"It took place at a time of night when a family were at home sleeping and could quite easily have had fatal consequences for those inside.
"We are treating this incident as an attempted murder and I am appealing to members of the public for information."
Mr Swift appealed to local garages and shops to report anyone buying petrol in cans or who returned home with burn injuries.
He also asked for anyone who saw, or has CCTV footage of, suspicious behaviour in the area of the house on Stonedene Court to get in touch.
:: Anyone with information is asked to contact HMET on 101, referencing Operation Pairglen and crime number 13190409679; report online at www.westyorkshire.police.uk/101livechat; or anonymously to Crimestoppers on 0800 555111.