The accident occurred around 4:30 am near Hindoli on the Jaipur National Highway when the pilgrims were on their way to offer prayers at the Khatu Shyam temple in the Sikar district.
"Six people were killed when an unknown vehicle hit their car, a Maruti Suzuki Eeco," Bundi's Additional Superintendent of Police Uma Sharma was quoted as saying by NDTV.
All these pilgrims were residents of Uttar Pradesh's Dewas.
"We have formed teams to trace the unknown vehicle," she said.
The senior police officer said they were trying to identify the victims.