The train Mewar Express was stationary before a red signal when another train, the Goa Express, collided with it from behind, police said.
The carriage hit was reserved for women and disabled passengers, but some other people may have been among the victims.
Rajendra Dutt Tripathi, a railway official, said initial reports suggested the Mewar Express was at a standstill because a passenger had pulled the emergency chain and that the driver of the Goa Express had overlooked a signal requesting him to stop.
"These are a matter of investigation and a final conclusion can only be reached after a detailed inquiry," he said.
The force of the crash was such that the engine of the Goa Express ended up being lodged inside the last carriage of the other train.
"There was a loud bang and we were suddenly thrown out of our seats," a passenger on the Mewar Express told the Press Trust of India news agency.
"People and luggage from the upper berths fell on us and there was panic everywhere," he said.
Saurabh Jain, another passenger, said rescue teams took more than an hour to
"The injured were wailing. There was no ambulance to ferry them to the nearest medical centres till about 6:45am," he told the Press Trust of India.
R D Vajpayee, chief spokesman for Northern Railways, said the company would pay 500,000 rupees ($10,800) to the families of the dead.
The state-run railway system carries 18.5 million people daily.
There are 300 accidents on the railways every year.