The sign was put in place by Cormac Seachoy, in 2014 before he was diagnosed with cancer "out of the blue" and died, aged 27, in December.
Harry Potter's creator J.K. Rowling has tweeted it was "one of the most beautiful Potter-related things ever".
The hospital plans to keep the plaque.
Cormac tweeted on 30 November 2014 that his plaque was in place, but it went unnoticed for 18 months.
It only came to light this week when the Bristol Post queried whether the hospital had granted permission for it to be there and discovered hospital chiefs were also unaware of its presence.
Finola Seachoy, Cormac's sister, said the appearance of the sign had also taken the family by surprise.
She said: "Cormac did it to put a smile on the faces of children who were ill, and it was with great sadness that he found himself in the very same hospital diagnosed with cancer out of the blue and with eight weeks to live, just over a year after he put the plaque up."
She said she was hoping to raise more money so the family could "create more of a legacy for Cormac, who was so much more than just the plaque".
A spokeswoman for the hospital, said: "The appearance of this plaque was a magical and mysterious event that we did not know anything about - but we are sure that our patients and their families will appreciate it.
"We do plan to keep this, but ask that any other magical beings that wish to erect plaques on our site do speak to us first so that the muggles amongst us can say thank you and look after and maintain these gifts".
Quidditch is a game, played by witches and wizards using brooms, in the Harry Potter series by J.K.Rowling.
The hoops sculpture is an interactive art installation created by artist Andrew Smith in 2001 and is called Lollypop-be-Bop.
A secret plaque claiming coloured hoops at Bristol Children's Hospital were the goalposts from the 1998 Quidditch World Cup in Harry Potter, has been found 18 months after it was erected.