An investigation is now underway after the incident on the platform at Grahamston Railway Station.
The incident occurred shortly before 7pm on Saturday and two hours after the match at Westfield between Falkirk and Hibs which the Edinburgh team won 2-1.
Video and images shot by train passengers have been shared on social media.
A spokeswoman for British Transport Police said: “We were called to football-related disorder at Falkirk Grahamston station at 6.50pm on Saturday – which is believed to have involved supporters from Hibernian Football Club and Falkirk football club.
“We are aware of video and images of the disorder being shared on social media sites.
“Investigations are ongoing, which is involving reviewing video footage and CCTV of the incident. No arrests at the moment.”
Anyone with information is asked to contact British Transport Police on 0800 40 50 40 or text 61016, quoting 499 of 6/8.