Sophie Jackson, from Knutsford near Manchester, was born with a congenital muscle disease, which means she is unable to swallow. She was rushed to hospital on 1 December after suffering a major cardiac arrest.
Her dad, Alan Jackson, requested people watch local news on 22 December for an update on his daughter.
BBC Northwest News made the announcement, which read: "Sophie Jackson from Cheshire has died. She was born unable to swallow. Her dad appealed last week for people to send cards to make her last Christmas special, and show her how much she was loved. She received over 10,000 cards."
Her dad confirmed the news and said she had died at 3.25pm on 22 December at the hospice.
He posted a message on Facebook quoting: "Someone I love and miss dearly is spending Christmas in heaven."
Sophie had been unconscious since being admitted to hospital on 1 December.
On 22 December, her dad made the difficult decision to take her to Francis House Hospice for children in Didsbury.
On 6 December, her dad appealed for Christmas cards on Facebook: "So the story is Sophie won't be home for Christmas and many months after.
"Jacko loves cards please share this post and let's see how many cards we get for her what could be her last Christmas."
Jackson said Sophie had received thousands of cards from all over the world, including Canada, Ireland and Australia.
Many have paid tribute to the young girl on Facebook.
Manchester City Football Club, who sent players to visit Sophie in hospital, wrote: "Huge respect to Phil Jones and Paddy McNair of Manchester United who supported seriously ill blues' fan, Sophie Jackson, who sadly, recently passed away...
"Football does separate us, to an extent, but ultimately, it brings us together."
Couple Channel Grief Into Retreat For Veterans
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Open Image ModalIn this July 16, 2014 photo, Jan and Terry Blumberg, left, talk with Richard and Mary Dunkley during lunch at Blumâs Landing in Ocqueoc Township, Mich. The Blumbergs used benefits and insurance money from their son Trevor's 2003 death in Iraq to help build Blumâs Landing. Now in its third year, the two-story home serves as a retreat for those fighting the war on terror. Veterans can stay at Blumâs Landing free of charge for up to five days. Richard Dunkley earned his familyâs stay by serving in Afghanistan. (credit:AP Photo/Mike Householder)
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Open Image ModalIn this July 16, 2014 photo, Jan and Terry Blumbergâs dog, Scrappy, stands on the front porch of Blumâs Landing in Ocqueoc Township, Mich. The Blumbergs used benefits and insurance money from their son Trevor's 2003 death in Iraq to help build Blumâs Landing. Now in its third year, the two-story home serves as a retreat for those fighting the war on terror. Veterans can stay at Blumâs Landing free of charge for up to five days. The Blumbergs promised their son they would take care of Scrappy, who is now 12. He was a puppy when Trevor Blumberg was killed. (credit:AP Photo/Mike Householder)
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Open Image ModalIn this July 16, 2014, photo, the back exterior of Blumâs Landing in Ocqueoc Township, Mich, is visible. Terry and Jan Blumberg used benefits and insurance money from their son Trevor's 2003 death in Iraq to help build Blumâs Landing. Now in its third year, the two-story home serves as a retreat for those fighting the war on terror. Veterans can stay at Blumâs Landing free of charge for up to five days. (credit:AP Photo/ Mike Householder)
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Open Image ModalIn this July 16, 2014, photo, the foyer area of Blumâs Landing is viewed in Ocqueoc Township, Mich. Terry and Jan Blumberg used benefits and insurance money from their son Trevor's 2003 death in Iraq to help build Blumâs Landing. Now in its third year, the two-story home serves as a retreat for those fighting the war on terror. Veterans can stay at Blumâs Landing free of charge for up to five days. (credit:AP Photo/ Mike Householder)