The fans threw glass bottles and chairs in the main square of Poznan at about 1 a.m. Sunday. Video footage showed chairs toppled on the square and police arriving in force to make arrests.
Police official Andrzej Borowiak says 10 Poles, three Irish fans and one Croat have been detained. Police are still trying to determine what role they had in the fight.
The violence comes after Russia fans attacked stadium security officers Friday night in Wroclaw.
Ireland and Croatia play their first Group C match on Sunday.