The 53-year-old was travelling on an 11pm Glasgow to Airdrie service when she was “touched inappropriately” by the attacker, British Transport Police said.
He then left the service at Coatdyke.
The suspect is described as about 5ft 2ins with short, dark hair. He was wearing jeans, a black and white blanket-style checked jacket and black gloves.
Detective Constable Finlay Bruce, the officer in charge of the enquiry, is appealing for a passenger who stayed on board past his stop to comfort the victim to get in touch.
He was carrying a guitar and was due to leave the train at Coatdyke.
Any other passengers on the train on Friday who can help identify the suspect are urged to contact British Transport Police officers on 0800 40 50 40.