Police and firefighting authorities are at the location trying to rescue people trapped in the building.
There were as many as six people trapped inside, a senior police officer said. Rescuers have been able to hear the sounds of at least two people inside, he added.
Several injured people have been rescued and are being treated in hospital.
Bellandur is a relatively new part of the city with many IT firms.
The under-construction building came down in a residential area.