Francesca Bimpson was one of four children injured in the fire at the property in Norwood Grove, Liverpool.
Two men, aged 43 and 45, have been arrested on suspicion of committing arson with intent to endanger life and have been bailed pending further inquiries.
After the fire on December 2 Francesca was taken to Alder Hey hospital where she died earlier.
Her sisters Anne-Marie, 17 months, Christina, eight, and 14-year-old brother Keiron were treated for the effects of smoke.
Their mother Eleanor Skelhorne suffered minor injuries and smoke inhalation. Francesca's dad, Kieron Bimpson, broke his legs jumping from a first-floor window.
Merseyside Police said the arson attack is being treated as a murder inquiry.
Superintendent Graham Yip, area commander for north Liverpool, said: "Francesca suffered horrible injuries in the fire and her family is devastated by her death.
"The person who did this is a coward and a murderer and we are determined to bring them to justice.
"If anyone saw anything or has any information about this incident, I would urge them to get in touch."
Anyone who can help the inquiry should call the police incident room on 0151 777 4065 or Crimestoppers on 0800 555 111.
