Police and paramedics were called at 08:20 BST (07:20 GMT) on Friday to Parsons Green station in Fulham.
Pictures show a white bucket on fire inside a supermarket bag, but does not appear to show extensive damage to the inside of the Tube train carriage.
Witnesses described seeing at least one passenger with facial injuries.
Others have spoken of "panic" as alarmed passengers left the train at Parsons Green station.
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