Those who do not keep at least one meter (3.2 feet) apart, or who meet in groups of more than 10 people outside of work or school, could face a fine of up to 10,000 Singapore dollars ($7,000) and/or up to six months' imprisonment, according to a Ministry of Health statement posted Thursday.
The new measures come into effect Friday and also include the same penalties for those who fail to stay in their accommodation if given a "Stay-Home Notice."
Such notices have been issued to certain inbound travelers as well as people with respiratory conditions flagged by medical practitioners.
On Wednesday, Singapore reported 73 new cases of coronavirus, its largest one-day increase in cases.
Since Monday borders have been closed to all short-term visitors and travelers transiting though the city.
The only exception is for Malaysians with Singapore work permits, who have been able to continue working in Singapore.
The government has urged employers to put in place measures to reduce close physical interactions between employees, and to facilitate telecommuting for employees to work from home.