Police and pro-Beijing groups ramped up calls for the British colonial-era law to be used for the first time in half a century after the city was rocked by the worst day of violence in 50 years during China’s National Day celebrations on Tuesday. Protesters and riot police clashed in more than a dozen districts, leaving more than 100 injured. Police also shot an 18-year-old protester in the chest.

The shooting brought people back into the streets to condemn the city’s police force Wednesday evening, targeting subway stations. Police were mostly absent from the streets until about midnight. Officials, who fear similar scenes this coming holiday weekend, have been running out of options to contain the unrest that has increasingly taken over the city and has sent the economy tumbling toward a recession.

The government is taking the unusual step of invoking the Emergency Regulations Ordinance to “end the violence and restore law and order to the streets,” one of the people familiar with the plan said. It would be the first time it has been used since the British colonial government invoked it to suppress 1967 leftist riots that shook the city during China’s Cultural Revolution.

Although the law confers sweeping powers on the city’s leader to deal with emergencies, Mrs. Lam is proposing very limited use, to stop people from wearing masks that have become a fixture of protests, the person said. Any further curbs on people’s freedoms would need separate regulations passed by the cabinet under the emergency law.

The law, first passed in 1922, allows authorities to impose curfews, censor media, search premises and take the control of ports and all transport. The government has been reluctant to use the powers, which some advisers have warned could steepen economic decline by appearing to undermine the rule of law that underlies the city’s role as a financial center and safe base for foreign businesses.

“Invoking this archaic law will only make the situation worse,” said Alvin Yeung, a pro-democracy lawmaker and barrister in the city. “This will not solve the turmoil—peace can only come if there is a political solution.”

Mrs. Lam last month pledged to withdraw an unpopular extradition law that triggered mass street protests in early June. The law would have allowed people to be sent for trial in China, which has a less independent justice system and where human-rights violations are common. But the withdrawal hasn’t lessened unrest. Protesters have four other demands that include a judge-led independent inquiry into alleged police brutality, pardons for those arrested at rallies and greater democracy.

Some foreign diplomats expressed doubts over the mask ban, saying it may be too impractical to implement or may backfire by furthering angering residents.

A number of countries, including Canada and France, and more than a dozen U.S. states have some form of antimask legislation. Last year, police in Georgia invoked an antimask law passed in the 1950s to arrest antiracism protesters. North Dakota passed an antimask law in 2017 in response to protests over an oil pipeline. A federal version called the “Unmasking Antifa Act” was introduced in Congress last year but failed to make it out of committee.

“Enforcement could be an issue,” one diplomat said, adding that such a proposal underscores how the Hong Kong government “has not many options left.”

Police in the city have increasingly refused to approve protest rallies and marches, but demonstrators have taken to the streets almost daily anyway, with crowds of tens of thousands most weekends. The gatherings often end in battles between police and front-line protesters, who wear gas masks to protect themselves from bombardment with tear gas. Many other protesters wear surgical masks to help hide their faces during assemblies, and some have started to wear Guy Fawkes masks seen at other protests around the world.

Surgical masks have been worn by people in Hong Kong in offices, streets and subways to prevent the spread of germs since the SARS epidemic killed hundreds in the city in 2003.

The law “affects our freedom of doing what we want to do and protecting ourselves,” said a 22-year-old student protester surnamed Wong.

“Someone will take photos of our faces—it may be a mainland supporter, a police officer or a journalist from pro-China media,” Mr. Wong said.

The student who was shot on Oct. 1—while wearing a gas mask—was charged Thursday with rioting and attacking a police officer. Tsang Chi-kin was shot at point-blank range as he and others swung bars at the officer.

Mr. Tsang, who remains hospitalized after undergoing emergency surgery, was represented by a lawyer during a court hearing.

Tuesday saw the city’s most violent unrest since the 1967 anti-British riots, with police firing around 1,400 rounds of tear gas, 900 rubber bullets, 190 beanbags, 230 sponge rounds and six live bullets in fighting the day before. More than 120 people were injured and 269 arrested—the highest daily totals so far in nearly four months of conflict.

The city’s influential Junior Police Officers’ Association called Wednesday for officials to adopt emergency laws to enable officers to better tackle protests. Officers were targeted by groups with metal bars and corrosive liquids, police chiefs said.

The association suggested a curfew law could be imposed in some places. The government considers a curfew unworkable in the city of seven million, a person familiar with the plan said. The city’s streets are busy day and night with workers commuting and has many districts with thriving late night bars and restaurants.

—Rachel Yeo and Chun Han Wong contributed to this article.

Write to Natasha Khan at natasha.khan@wsj.com