One person was arrested after a match between Longford Town and Bray Wanderers in the League of Ireland on Friday night.
Videos online appeared to show some fans engaged in anti-social behaviour at Bishopsgate Stadium outside Longford.
The League of Ireland and the FAI said they strongly condemned the behaviour of "a small number" of spectators in the away section of the stadium.
They said: "We are now working closely with the Gardai and both clubs to ensure those responsible are held accountable for their actions.
"The FAI has a zero tolerance policy towards this type of behaviour and will take further action once the Garda investigations are concluded.
"The safety of all players, fans and stewards is of paramount importance to the League of Ireland and the FAI."