The girl, who cannot be named for legal reasons, pleaded guilty to manslaughter by diminished responsibility.
Katie was found with severe lacerations to her neck and chest on a playing field in Woodthorpe, York, on 9 January. She died later in hospital.
The girl did not speak as she entered her plea via video link at Leeds Crown Court. She denied a separate charge of murder.
Nicholas Johnson QC, defending, asked the court if the charge of murder could be put to the girl again and she wrote her plea on a piece of paper.
Her solicitor told the court: "I can confirm she has indicated not guilty to murder but guilty to manslaughter."
Graham Reeds QC, prosecuting, said: "We are going to accept that plea of manslaughter by diminished responsibility."
Katie was a pupil at Westfield Primary School in the Acomb area of York.
In the days after Katie's death Tracey Ralph, head teacher at the school, described her as a "kind and thoughtful child who was well-liked by both pupils and staff".
Katie's funeral service took place at York Minister in February.
More than 300 people attended the service, which was led by the Archbishop of York, Dr John Sentamu.
Her coffin was decorated with characters from the Dr Seuss children's books.
Image copyrightPAImage captionMore than 300 people attended Katie's funeral
Image copyrightPAImage captionHer funeral service was held at York Minster
During the funeral service Katie's uncle described her as a "smart, fun, beautiful child".
He said she had selective mutism, but that it did not stop her from having fun.
"Her family were her world," he said.
"She loved her mum and dad but she was definitely described as a daddy's girl."