The 40-strong troupe were returning from a performance late on Sunday when their bus steered off a hilly road and into a 76-metre (250-foot) gorge in Deogarh district of Odisha state.
"Twenty-seven people lost their lives and around 11 were injured," Sarah Sharma, Deogarh's superintendent of police told AFP. "One of the dead was a child".
An investigation has been ordered, but Sharma said the driver of the chartered vehicle appeared to have taken a sharp turn too quickly.
Emergency workers had to use ropes to pull the injured people out of the gorge.
Fatal traffic accidents are common in India, which has some of the world's deadliest roads with more than 200,000 fatalities annually, according to the World Health Organization.
A packed passenger bus plunged off a bridge into a river in western India in February, killing at least 37 people in one of the deadliest road accidents in recent years.
In October, 15 members of a wedding party, including three children, were killed when a vehicle they were travelling in collided with a bus in the south of the country.
