Television pictures showed fire breaking out at the front of the outdoor stage during a performance by dancers. It quickly spread, fanned by high winds, licking the sides of a scaffolding rig and lighting up the night sky.
Thousands of spectators, among them dignitaries including the chief minister of the host state of Maharashtra, were evacuated safely, eyewitnesses told Times Now television.
There were no reports of fatalities, according to organisers and the Home Ministry in New Delhi. Fire tenders were rushed to the scene, where the blaze was being brought under control.
The fire is likely to overshadow the message that India is open for business that Modi wanted to send when he opened the investor jamboree on Saturday.