The protester was shot when the police used live ammunition for the first time, near Hoi Pa Street in Tsuen Wan district, the South China Morning Post reported. A video of the man surfaced on Facebook where he was seen groaning on the ground and saying: "My chest is in pain, take me to the hospital!"
According to a friend, the man was in critical condition at the Princess Margaret Hospital.
Tens of thousands defied a police ban to march through central Hong Kong, and thousands gathered in other parts of the city. Organisers and protesters said the 70th anniversary of communist rule should be a "day of grief" not celebration.
People took to the streets in at least six other districts also, blocking roads in some areas. According to reports, 15 people were hospitalized during the clashes. The police fired teargas and rubber bullets to disperse the protesters, themselves armed with umbrellas, projectiles and petrol bombs.
The police also advanced with water cannon.
A police officil said that another two rounds were fired at the junction of Waterloo Road and Nathan Road in Yau Ma Tei after a group of protesters attacked a police van.
Earlier in the day, government officials attended an indoor flag-raising ceremony at the Hong Kong Convention and Exhibition Centre to mark China's National Day, away from the crowds who were protesting on the streets of the city plagued by democracy protests since June.
Twenty-five out of 91 MTR stations were closed and many shops and more than 25 shopping malls around the city shuttered for the day. Some 6,000 officers were deployed in the territory. An annual fireworks display had earlier been cancelled.
The Hong Kong police warned the public of violent riots across the territory, and took to social media to "strongly condemn" the protesters.
"Currently, there are rioting acts across Kowloon, Hong Kong Island and the New Territories. Rioters have started fires and committed mass property damage, injuring many people," the police posted on Twitter.
"The police urgently appeal to every member of the public to stay in safe places, avoid going outdoors and stay tuned to the latest situation."
Earlier in the day, the police also tweeted that protesters had thrown "corrosive fluid", injuring several police officers.
Hong Kong has been witnessing mass demonstrations since June, sparked by a contentious extradition bill, but the movement has since morphed into a wider and violent anti-government movement channelling residents' anger and frustration at the erosion of their rights under Chinese rule.
China on Tuesday marked 70 years since the founding of the People's Republic of China with a military parade which was the largest in the country's history.
The parade which was held in Tiananmen Square was also attended by Hong Kong's Chief Executive Carrie Lam.
( With inputs from IANS )