The 15-year-old local boy is charged over the incident at Glencoe Gardens in Kippax in the early hours of Tuesday.
Firefighters were called at about 1.47am with the family of seven – a man, aged 39, a woman, aged 48, and their five children, aged 9 to 19 – believed to be inside.
The family were out of the house before fire crews arrived but a 16-year-old girl suffered serious burns and was taken to in Pinderfields Hospital in Wakefield.
She was described as being in a critical but stable condition today.
The couple and the 19-year-old son also required treatment for burns and smoke inhalation but were recovering in hospital today.
Enquiries are ongoing.