The police say a case has been registered against "unknown people" for the car-burning.
The carolers - about 30 of them - were picked up by the police from a road as they were moving around the town singing carols for Christmas.
Eight priests who went to the police station to ask about the detained carolers were also held back. It was the car they used that was burnt by activists.
The carolers are from the St Ephrem's Theological College in Satna.
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