Zika, which has been detected in 58 countries including hardest-hit Brazil, causes only mild symptoms for most people, such as fever and a rash.
But in pregnant women, it can cause microcephaly, a deformation in which babies are born with abnormally small brains and heads.
As of Tuesday Singapore had confirmed 82 locally transmitted cases of Zika infection.
The initial cases were reported at the weekend from the Aljunied area and since then, the neighbourhood has been in the spotlight.
Environment ageny inspectors armed with cans of insecticide and torchlights, as well as pest control teams, have become a daily sight.
At least five of 26 new cases confirmed late on Tuesday were detected outside the initial cluster in the Aljunied area in the southeast of Singapore, the health ministry and National Environment Agency (NEA) said in a joint statement.
Australia, Taiwan and South Korea issued travel warnings, and Singapore advised pregnant women to take a free Zika test if they showed any symptoms or if their partners tested positive.
“This is regardless of whether they have been to Zika-affected areas,” the statement said.
The outbreak and advisories come as the tourism industry in one of the world’s busiest travel hubs already faces weak global economic growth. Singapore’s Tourism Board said it was premature to consider any impact on the sector, adding it remained a “safe travel destination”.
More than 55 million people pass through Singapore’s Changi airport every year. In the first half of this year, tourism arrivals topped 8 million, around 1 million more than a year earlier.
Singapore reported its first case of locally-transmitted Zika at the weekend, and the number of confirmed infections has risen steadily since then. At least three dozen patients have made a full recovery.
Neighbouring Malaysia and Indonesia have stepped up protective measures, introducing thermal scanners at airports and border checkpoints with the island state.
Singapore residents responded to government calls to be vigilant and to take precautions against mosquito bites.