Millie Martin was injured in an alleged assault and died in intensive care.
Serious crime unit officers in Northern Ireland were granted an extra 36 hours to question the arrested man aged 30.
Millie died at Belfast's Royal Victoria Hospital. She had been transferred from a local hospital after being hurt in Enniskillen, Co Fermanagh, on Friday.
Last night police refused to reveal the results of a post mortem examination.
Millie's mum Rachael, 25, was said to be devastated. A family spokeman said: "We are deeply heartbroken by the death of our beautiful little Millie.
"The entire close-knit family are numb with pain.
"We are going through unbearable grief."
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