York Chow, Hong Kong's health secretary, said authorities became concerned after five classmates of the 7-year-old boy who died had also been hospitalised.
The five are continuing to receive treatment and said to be in a stable condition.
Officials have said that some of the boy's classmates were suspected of suffering from the flu, and the government closed the school earlier this week.
Explaining the decision to close schools, Chow said he acted quickly because "when you wait until you have all the data, it's too late."
Most schools had in any case been due to close in about a week's time for the Easter holiday.
The illnesses have not been linked to the deadly H5N1 bird flu virus, which has been detected in birds in Hong Kong, and health experts have cautioned the public that there is no reason to panic.
Although currently thought to be hard for humans to catch, scientists fear that H5N1 could mutate into a more easily transmissible form.
Nonetheless the decision on Wednesday to close schools across the territory has brought back memories of the 2003 outbreak of the Severe Acute Respiratory Syndrom (SARS) virus.
The virus which first emerged in southern China in late 2002 killed 299 people in Hong Kong and badly damaged the territory's economy.
At the time government officials were criticised for not acting quickly enough.
The Hong Kong government says it has asked one of its top scientists, Yuen Kwok-yung, who studied the SARS outbreak, to head a panel of experts investigating the flu outbreak.