He also said the farm and neighbouring poultry operations were declared part of an infected zone, and that about 80,000 birds in the area would be killed to prevent the spread of the disease.
Hong Kong's biggest bird flu outbreak was in 1997, when the H5N1 strain travelled to humans and killed six people.
It prompted the government to slaughter all 1.5 million poultry in the territory.
In 2001, the government also carried out a massive poultry slaughter, killing 306,000 birds in wholesale and retail markets and 951,000 in local farms to eradicate an outbreak of bird flu.
The findings in Hong Kong came as the World Health Organisation (WHO) announced that a two-year-old girl in Indonesia had died after being infected with a deadly form of bird flu.
The UN health agency said that the child, from East Jakarta, developed symptoms on November 18 and died 11 days later.
The WHO also said that a 9-year-old girl from Riau province tested positive on November but has since recovered.
The two cases take Indonesia's official tally of bird flu in humans to 139, according to WHO figures.
At least 245 people have died of bird flu worldwide since 2003, the health body says.