No one was injured in the fire, which broke out at around 4.30 am in one of the cars of the train on the Western Railway route, and immediately put out, a senior police official said.
The incident took place when the train was static between Marine Lines and Churchgate stations.
"We suspect it to be work of some mischievous person," the official said.
One "mentally unstable" person has been detained by Government Railway Police (GRP) in this connection, he said, adding the matter is being probed.
