The Malaysian woman had made a brief trip in late August to visit her daughter, who has already been confirmed as having the Zika virus, Malaysia's health ministry said in a statement.
After returning to her home near Kuala Lumpur, the woman fell ill and was diagnosed with "suspected" Zika, based on a urine test. Full confirmation via blood tests is pending.
"The source of infection is suspected to have occurred in Singapore," the statement said.
It causes only mild symptoms for most people such as fever and a rash, but pregnant women who catch it can give birth to babies with microcephaly, a deformation marked by abnormally small brains and heads.
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Singapore is one of Asia's cleanest cities with high healthcare standards, but is a densely populated tropical island with heavy rainfall and has a chronic problem with dengue fever, also spread by the same Aedes mosquito.
Authorities say 115 people have now tested positive for the virus, including a pregnant woman and 57 foreigners living and working in the city-state.
Among the foreigners infected, 23 are from China, 15 are from India and 10 from Bangladesh, the health ministry said today. The rest are from Malaysia, Myanmar, Indonesia and Taiwan.
Singapore health officials on today sought to reassure the international community that the disease is under control after the United States and Britain joined Australia and Taiwan in advising pregnant women to avoid non-essential travel to the city-state.
"I don't think there's a need for us to press the panic button," said Derek Ho, director-general for public health at the National Environment Agency (NEA).
Since the first locally-transmitted case was reported on Saturday, some 5,800 homes and shops have been inspected for mosquito breeding sites with 49 habitats destroyed, the NEA said.
"Our best defence is to eradicate mosquitos and destroy breeding habitats, all over Singapore," Prime Minister Lee Hsien Loong said in a Facebook post today.
Indonesia and Malaysia have intensified monitoring of border points for passengers arriving from Singapore.
Tropical Malaysia - which already has also struggled in recent years to control the spread of dengue fever - has been bracing for Zika after Singapore last weekend reported a surge in cases.