Chief Executive Lam urged Hong Kong people to avoid gatherings ahead of next week's Lunar New Year as officials grappled with an outbreak of the highly-infectious omicron variant in Kwai Chung, north of the city's Kowloon peninsula.
"We are worried that the exponential growth of cases that we have seen in other parts of the world is now happening in Kwai Chung," Lam said.
The situation is testing Hong Kong's "zero COVID" strategy focused on eliminating the disease, with schools and gyms already shut, restaurants closing at 6 p.m. (1000 GMT) and air travel with many major hubs severed or severely disrupted.
Speaking after meetings with health officials, Lam said that there was only a "slim chance" those city wide restrictions could be lifted on Feb. 4 as planned.
She said that a second Kwai Chung apartment block, home to more than 2,000 people, would be shut down for five days.
On Friday, officials shut down a first Kwai Chung building for five days after more than 20 cases were linked to it, with food delivered from outside three times a day and mass testing underway.
By Saturday, officials recorded some 105 cases in Kwai Chung, including confirmed and preliminary positive tests.
In total, some 16 buildings in the area would face various restrictions and compulsory testing, affecting some 35,000 residents, Lam added.
Local media reports on Saturday said that officials were considering tighter city-wide restrictions but none have yet been confirmed.
On Tuesday, officials ordered the killing of about 2,000 hamsters from dozens of pet shops after tracing a coronavirus outbreak to a worker at a shop, where 11 hamsters later tested positive for COVID-19.
Lam said that cases involving the Delta variant were also rising because of the hamster outbreak.
"I understand that pet owners are unhappy ... the biggest public interest is to control the pandemic," Lam said.
Thousands of people have offered to adopt unwanted hamsters amid a public outcry against the government and its pandemic advisers.