She died in hospital after her family's home was burnt down with her inside.
Reports from Iraq suggest that the child was in the shower when her mother was asked to pay a special religious charge handed out to minorities like Christians, Shia and Alawite Muslims.
Her mother said she would pay, but reportedly asked the militants to wait until her daughter had come out of the shower.
The fighters refused and set fire to the bathroom that the child was inside.
Human rights advocate from Road of Success, Jacqueline Isaac, told The Telegraph: "The ISIS [Islamic State) foreign fighters were at her door and they told her 'you have two choices, you are to leave now or you are to pay the jizya'.
"She said 'I will pay, give me a few seconds my daughter is in the shower'.
"They said 'you don't have a few seconds' and they lit the house with a torch from the bathroom the daughter was showering in."
Ms Isaac was speaking during a conference on persecuted Christians in New York.
She told the audience that the daughter escaped, but died in hospital after her injuries.
She said the child asked her mother to forgive those that hurt her.
"The daughter had four degree burns and the mother took her daughter, scrambling, doing anything to save her.
"Rushed her to the hospital and her daughter died in her arms. The last thing her daughter said: 'Forgive them,' " she said.
Islamic State seized Mosul, Iraq's second largest city in June 2014.