The woman arrived from New York early on Tuesday and was not picked up by thermal scanners at the airport as she did not have a fever then, the government said in a statement.
She is currently in a stable condition.
Authorities also say they were tracing the flu patient's close contacts and said they would be quarantined and treated with anti-viral medication.
Singapore health officials have been warning residents for weeks to prepare for an outbreak in the city-state.
Cruise ship quarantined
|Over 50 cases of H1N1 flu in Australia have been confirmed EPA]
In Australia meanwhile health officials sought to defend the decision to allow around 2,000 cruise ship passengers to disembark in Sydney on Monday and head home, despite at least 14 passengers being diagnosed with the virus.
Another 172 people on board the Pacific Dawn were reported to have shown flu-like symptoms or reported contact with someone who did.
All were advised to go home and self-quarantine themselves for seven days.
The Pacific Dawn, along with its current passengers and crew, has since been quarantined near Willis Island, east of the Queensland city of Cairns, after three crew members exhibited flu-like symptoms.
Speaking to reporters on Wednesday Nicola Roxon, the health minister, said border controls would be tightened at Australian ports but defended the release of the passengers.
The announcement came as the number of confirmed Australian cases of the new flu strain, formerly known as swine flu, more than doubled overnight to 59.
"I understand that there are some questions being asked and some level of frustration that perhaps people should have been held while more tests were being done," Roxon said.
"We have to try and have a proportionate response, and holding 2,000 people or trying to put them in some sort of isolated circumstances would have its own difficulties."