They must self-isolate until their test result is declared negative.
Unvaccinated children aged under 12 years will be permitted to enter the city state.
Flights from Singapore will only land at Sydney or Melbourne.
Singapore recently opened travel corridors with other nations including the US, Britain and Germany.
The announcement overnight comes amid rising COVID-19 cases in Singapore, despite the country having full vaccination rates of more than 80 per cent.
During the latest reporting period, the country recorded more than 2800 cases, although nearly all were described as mild or asymptomatic.
About 25,000 Australians live in Singapore and the South East Asian nation is an important destination for business travellers and students.
Singapore’s Changi Airport is also an important connecting point for onward flights to other major international destinations.
Australia is preparing to open to uncapped overseas arrivals on November 1.