The baby girl died from a fractured skull at Booth Hall Children's Hospital on Monday.
She had been taken there from her home at about 2200 on Friday.
It is thought the girl had been the child's babysitter, who had helped the toddler's mother before.
It is understood that the girl raised the alarm by contacting the baby's aunt, who went to the house, in the Crumpsall area of Manchester, to find her niece collapsed in a cot with a nose bleed.
The aunt desperately attempted resuscitation before the toddler was rushed to hospital.
Police confirmed that the girl was held for questioning on Saturday. She was released on police bail pending further inquiries.
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