Flight 423 was escorted safely back to the airport by Singapore's air force and touched down at about 8 am, The Straits Times quoted the police as saying.
The police searched the Boeing 777-300ER that carried 263 people onboard, but did not find any suspicious item.
All passengers, except for a woman and a child who were held back for questioning, disembarked safely and had to undergo security screening before they could leave.
Preliminary investigation showed that the airline had received a call after the plane left the Mumbai airport on Monday at 11.35 pm. The caller claimed that there was a bomb on the plane.
An airline spokesman told The Straits Times: "Singapore Airlines confirms there was a bomb threat concerning SQ423 operating from Mumbai to Singapore... We are assisting the authorities with their investigations and regret that we are unable to provide further details."