A Tuen Mun Hospital spokesman said the boy was admitted to its paediatric intensive care unit on January 20 after being treated at the accident and emergency department of Tin Shui Wai Hospital the same day.
Paediatricians gave the boy Tamiflu an antiviral medicine for the treatment of the illness antibiotics and antiepileptic drugs.
He was diagnosed with acute necrotising encephalitis and needed a mechanical ventilator to help him breathe.
His condition continued to deteriorate and he died at 7pm on Monday.