Hong Kong officials said a man carrying a pro-independence flag is the first person to be arrested in Hong Kong after the new "anti-protest" law imposed by Beijing has come into effect.
Police have used pepper spray to disperse some protesters gathered to mark 23 years since British rule ended, reports BBC.
The national security law targets secession, subversion and terrorism with punishments up to life in prison.
Critics say it stops some freedoms meant to be guaranteed by China.
Hong Kong was handed back to China from Britain in 1997, under an agreement supposed to protect certain freedoms for at least 50 years.
"[China] promised 50 years of freedom to the Hong Kong people, and gave them only 23," US Secretary of State Mike Pompeo said.
"The [new law] is considered the most important development in relations between the central government and Hong Kong since the handover," said Chief Executive Carrie Lam.
At the same time, a Chinese official bristled at foreign critics, asking them, "What's this got to do with you?"
"We Chinese will not be scared by anyone," said Zhang Xiaming of the Hong Kong and Macao Affairs office of the State Council. "Gone are the days when we had to take cues from others."
Hong Kong police said the arrested man was carrying a "Hong Kong Independence" flag as they warned certain slogans and banners might constitute serious crimes under the new legislation.