Natasha Sultan admitted a charge of infanticide when she appeared before a judge at Hull Crown Court.
Her daughter Amelia-Lilly was taken to hospital from her home in Welton Grove, Hull, in October last year.
She was suffering from a head injury and later died.
Sultan was due to go on trial for murder on Monday but the prosecution accepted her plea to the infanticide charge.
Judge Jeremy Richardson QC accepted the balance of her mind had been disturbed at the time.
Detective Chief Inspector Alistair McFarlane, of Humberside Police, said it had been "a very distressing" case to investigate.
He said: "Amelia-Lilly died as the result of head injuries, inflicted by her mother in the early hours of October 8 last year.
"Police officers have been in regular contact with Amelia-Lilly's father and his family.
"This is a tragic event, which has been difficult for the family to come to terms with and our sympathies go out to them.
"The police investigation has taken a considerable time to prepare, due to the number of experts who have been consulted. It has been a very distressing case to investigate."
Sultan will be sentenced for the killing on Tuesday.
God! how can you kill your onw child?
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