Scoot flight TR16 to Perth departed Singapore at 4:11 p.m. (0811 GMT).
But about one hour into the flight, "a precautionary decision was made to turn the aircraft back to Singapore due to a bomb threat," Scoot, the budget arm of Singapore Airlines, said in the statement.
"The Republic of Singapore Air Force (RSAF) was activated to escort the aircraft back to Changi Airport. Emergency services were also activated," the airline added.
Scoot said the flight landed safely about two hours after takeoff, and security checks were carried out.
The airline said it was assisting authorities with investigations but said it was unable to provide additional details as "this is a security matter."