The British Transport Police were called out to the incident at about 03:00 on Thursday.
Officers met the train in Carlisle and arrested a 21-year-old man on suspicion of fire raising and theft.
The BTP said he was being transferred back to a base in Scotland to be dealt with under Scots Law.
London-based officers met the train when it arrived at Euston railway station at about 09:00 in order to make further inquiries with passengers and staff.
A man has been arrested in connection with a small fire on board a Caledonian sleeper train reported as it was travelling through Lockerbie station.