The attack happened as the 24-year-old was travelling on the 9.40pm Edinburgh Waverley to Aberdeen service on Monday.
The woman, from Aberdeen, was walking through the carriage when a man punched her knee.
Police want to trace a suspect, thought to be aged in his 60s, who alighted from the train at Montrose station at around 11.20pm.
He is described as about 5ft 6in and was wearing a blue baseball cap, a grey jacket and trousers and white training shoes. He was also carrying a blue holdall.
Constable Ashley Forbes, of British Transport Police, said: "There appears to be no explanation for this unwarranted assault and I am anxious to speak with anyone who can help our inquiry by providing information which can help identify the suspect."
Anyone with information can contact British Transport Police on 0800 40 50 40.
Meanwhile, a gang of teenage boys subjected a 17-year-old student to a torrent of verbal abuse on a busy train.
British Transport Police (BTP) officers are appealing for information after the young woman was verbally abused by the three boys, who are said to be aged between 13 and 15.
Some of the verbal abuse was of a sexual nature, BTP said.
The incident happened yesterday on a train travelling between Cartsdyke and Greenock West stations in Inverclyde.
The girl was travelling in the front coach of the 5.06pm Glasgow Central to Gourock service and the boys got on the train at Cartsdyke station around 5.45pm.
They left the train when it arrived at Greenock West.
Constable Robert Johnstone of BTP said: "The victim was understandably upset and intimidated by the boys' behaviour.
"The train would have been busy at the time and I am urging anyone who was on the service or at either station and has information which can help identify those involved to get in touch."
The boys responsible were wearing casual clothes and one had short reddish hair while the others had short dark hair.