The incident came as thousands of people demonstrated in defiance of a protest ban for the 70th anniversary of Communist rule in China.
Though people have been shot by rubber bullets in previous protests, this is the first injury from a live round.
In the Chinese capital Beijing, 15,000 soldiers paraded with advanced military hardware to mark the anniversary.
Nearly four months of protests in Hong Kong have challenged Chinese President Xi Jinping's vision of national unity.
Earlier, the Chinese flag was raised at a special ceremony in the territory. Security was tight and the 12,000 invited guests watched the event on a live video feed from inside a conference centre.
On what is being described by protesters as a "day of grief", people took to the streets in central Hong Kong and at least six other districts, blocking roads in some areas.
At least 66 people were injured during the clashes, as police fired tear gas and protesters threw petrol bombs. Two people were in a critical condition and two others were seriously injured, the Hospital Authority said.
According to local media, at least 180 people were arrested.