A fight broke out on Sunday evening at the asylum seeker reception centre in Kofinou between old and new residents.
The fray, involving around 100 people, started at around 8pm. The rival groups dispersed at the sight of the police.
A 19-year-old Palestinian man from Syria was slightly injured during the incident.
Reports said the row started over a disagreement concerning the ball the children were playing with.
A strong police force was still at the centre on Monday.
The centre currently houses 277 people, including a number of refugees rescued off the coast of Cyprus on September 5.
The group of 115 were rescued 74 kilometres off the coast of Larnaca. They had sailed from Tripoli, Lebanon, and were trying to reach Greece.
The engine of the vessel broke down and they had been at sea for three days when they were rescued.