Authorities authorized a hamster cull earlier this week in response to the outbreak.
The outbreak of Delta cases was traced to a pet store employee, prompting officials to test hamsters, with some testing positive.
Hong Kong is committed to eradicating the disease with a "zero-Covid" policy.
Lam encouraged residents to avoid gatherings ahead of next week's Lunar New Year, citing the territory's ongoing battle with an Omicron variant outbreak.
The Asian financial powerhouse has some of the strictest coronavirus regulations globally since it adheres to China's stringent zero-Covid legislation.
"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," she is quoted as saying by the news agency Reuters.
Kwai Chung is a densely populated residential neighborhood located north of Hong Kong's Kowloon peninsula.
She added that cases of the Delta strain were also increasing as a result of the hamster outbreak.
"I understand that pet owners are unhappy... the biggest public interest is to control the pandemic," she explained.
Approximately 2,000 hamsters and other small mammals are scheduled to be killed as a result of the outbreak associated with the pet business. Officials believe it may be an instance of Covid transmission from animal to human.
Countless have signed a petition against the idea, and thousands more have pledged to help preserve the creatures via social media.
Sars-Cov-2, the virus that causes Covid-19, can be contracted by animals such as dogs, cats, ferrets, and rodents, all of which are widely kept as pets. However, there is no conclusive proof that pets can easily transmit the virus to humans.
In late 2020, millions of farmed mink were killed in Denmark due to concerns about virus mutations arising within the animals.