"We have kept the outbreak under control but looking at the trend, I am anxious that unless we take further steps things will gradually worsen or another big cluster may push the thing over the edge", the prime minister said during his address to the nation.
Currently, Singapore has recorded 1,114 confirmed cases of COVID-19 infection at the time of writing, with 5 deaths reported.
In Monday's parliamentary session, a number of new measures will be put into legislation as well, Mr Lee said, including a requirement for landlords to pass on property tax rebates fully to their tenants.
He urged Singapore to stay at home as much as possible, avoid socialising with others beyond their own household, and confining gatherings to those living in the same household.
"Go out only to do essential things", he said. "It is as simple as that", he said.
The Southeast Asian nation has adopted some social distancing measures to curb the spread of the virus, but schools, offices and restaurants remain open.
Mr Lee acknowledged that the new measures "will impact our workers and businesses severely" on top of "an already hard time". Those who break "circuit breaker" rules will be subject to fines of up to SGD10,000 (~RM30,351) and/or six-month jail term.
The measures, which include the closure of most workplaces, will last for at least a month. "Let's hunker down and beat the virus together".
Singaporeans can also still "buy food from your favourite hawker centres or coffeeshops" for takeaway to be enjoyed at home with their families "rather than hang out and eat outside with your friends", he said.
In a Facebook post, the prime minister said: "The current situation is under control, but we want to take a few more steps now".
Japan has so far been spared the sudden surge seen in parts of Europe, the United States and elsewhere.
Yuriko Koike, the Governor of Tokyo, said that Japan declaring a national state of coronavirus emergency would send a "strong message" that could help dodge an explosive outbreak.