The protester was shot when the police had fired in the air near Hoi Pa Street, the South China Morning Post reprted.
A video of the man has surfaced on Facebook where he is 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.
A police source 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 parked there.
A massive banned "national grief" march is moving from Victoria Park in Causeway Bay to Central, and protesters appeared intent on continuing their journey toward Beijing's liaison office in Sai Ying Pun.
Tear gas has been fired in Wong Tai Sin, Sha Tin and Tsuen Wan while street fights broke out earlier in Tuen Mun.
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 a crowd who were protesting on the streets of the city plagued by democracy protests since June.
Twenty-five out of 91 MTR stations have closed and many shops and more than 25 shopping malls around the city have shuttered for the day.
China on Tuesday marked 70 years since the founding of the People's Republic of China (PRC) 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.
Hong Kong has emerged from 17 straight weekends of protest, triggered by the now-withdrawn extradition bill, which would have allowed criminal suspects to be sent back to mainland China.
( With inputs from IANS )