Lesma-Rose Wibier was pulled from the blaze at the property on Gateshead Close, Rusholme, on Sunday afternoon, Greater Manchester Police said.
She later died from her injuries in hospital.
A 44-year-old woman, who police say knew the child, was arrested on suspicion of arson with the intent to endanger life, and has been rearrested on suspicion of murder.
She has been detained under the Mental Health Act and is awaiting further assessment, Greater Manchester Police said.
Paying tribute, the girl’s family said: “Lesma-Rose was the star of the family. Anyone who knew her knew she was the most beautiful girl inside and out.
“She always had a smile on her face and could put the same on others.
“She was such a smart and intelligent girl in her own unique ways, and she will be deeply missed by anyone who was blessed to meet her.”
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