The authorities are monitoring places outside the Aljunied Crescent and Sims Drive area - where the Zika cases emerged - after finding that some who contracted the disease either live or work elsewhere.
Khatib Camp, Sembawang Drive, and several worker dormitories are among those on the list.
"Given that the Zika virus is spread by the Aedes mosquito vector, MOH cannot rule out further community transmission in Singapore, since some of those tested positive also live or work in other parts of Singapore," the Ministry of Health and National Environment Agency (NEA) said in a joint statement.
Of the 41 confirmed cases of Zika, 36 are foreign construction workers from a site in Sims Drive.
NEA inspected their on-site quarters and two other worker dormitories in Kranji Road and Senoko South Road on Saturday. One mosquito breeding site was found at Kranji.
Since Saturday, NEA has stepped up its anti-mosquito measures - which include fogging and increased frequency of drain flushing - in the affected area and implicated dorms.
Such measures have also been taken in other dorms where the site's workers live, in Joo Chiat Place, Toh Guan Road East and Lorong 101 Changi.
Of the other five cases, one is a full-time national serviceman at Khatib Camp who lives in Sims Drive. Another is a 30-year-old Singaporean man who works at the construction site but lives in Sembawang Drive. The rest are a Malaysian woman who lives and works in the cluster area, a retiree - the NSF's father - who lives there, and a 44-year-old unemployed Singaporean who lives in Sims Drive.
The authorities said they "have verified with Khatib Camp that there were no symptomatic cases to date".
Last night, NEA began distributing insect repellents and leaflets with information on Zika to Sembawang Drive residents, having already done so in the affected area. MOH is carrying out Zika testing on other people with symptoms of fever and rashes who live and work in the main affected area, as well as the other areas of concern.