Greater Manchester Police were called shortly after 2.30pm on Sunday and, together with the ambulance service, found the child had been attacked with a knife.
Emily suffered "extremely serious injuries" and sadly passed away despite the best efforts of her family and medical responders
The 30-year-old woman arrested at the scene on suspicion of murder was assessed by specialist medical staff and detained under the Mental Health Act.
She remains in a highly secure facility.
Paying tribute to Emily, her parents said: “Emily was 7-years-old, our only child and the light of our lives.
“She was always full of joy, love and laughter.
“Emily had such a cheeky smile and was beautiful inside and out. She had a heart as big as her smile.
“Emily was never happier than when she was spending time with her family and friends, she was our own little social butterfly.
“Emily had a passion for the outdoors and loved to play any sport, even when she was wearing her pink sparkly dresses!!
“We are beyond devastated that this random act of violence means that we will never get to see our beautiful little girl grow up into the wonderful young lady she was showing such promise of becoming.
“It is truly heart breaking to wake up to a world without Emily in it and we cannot comprehend why this has happened.
“We would like to thank the members of the public that assisted us in the park and express our gratitude to the emergency services for doing their upmost to save Emily’s life.
“Thank you to everyone for their kind messages of support and for continuing to respect our privacy at this difficult time.”