Seven-year-old Preston Flores from Aberdeen suffered burns to much of his body in an incident believed to have involved petrol.
It is understood the little boy was playing with friends in Bedford Avenue in the east of the city when he was engulfed by flames on Friday.
He was taken to the Royal Hospital for Sick Children in Edinburgh for treatment but died yesterday morning.
His mother, Luisza, said in a statement: "He meant the world to his family and will always be deeply missed and loved. Preston was a special little boy and his loss has ripped our family apart.
"On behalf of our family, I would like to thank everyone for their support but would ask that we are now allowed to grieve in peace for Preston."
First Minister Alex Salmond said last night: "This is a tragic time for the young boy's family, for the staff and pupils at Sunnybank School, and for the many friends of Preston Flores. Our thoughts are with them all."
Police responded to reports of a boy on fire on Bedford Avenue at around 2pm.
Officers are investigating whether petrol was involved but say there is no suggestion the youngster was the victim of a deliberate act.
Preston was a primary three pupil at Sunnybank School where acting headteacher Michelle McKay said he had lots of friends.
She said: "He was a fun-loving boy with a great sense of humour and lots of friends.
"This is a tragic time for his family, for the school and for everyone connected to it. We are all so saddened by what has happened."
Police said a report will be sent to the procurator-fiscal in line with usual procedure.
Detective Inspector Lorna Ferguson, from Police Scotland, said: "Our thoughts are with Preston's family, friends and the Bedford community at this sad time."
Leader of Aberdeen City Council Barney Crockett said: "My own thoughts are with the little boy's family."