A migrant was injured during fighting at the makeshift refugee camp in Piraeus early on Monday.
The man, a migrant from Lebanon, as hurt when a fight broke out over a missing mobile phone. He was taken to the hospital for treatment.
Authorities have managed to reduce the number of migrants at the camp over the last few days, transferring hundreds to a new facility at Skaramangas, west of Athens.
The official data published by the Greek government on Monday morning showed that there were 3,758 people at the Piraeus port out of a total 53,824 at camps all over Greece.
About 500 more people are due to be taken by bus from Piraeus to Skaramangas on Monday. The new site can host around 2,500 people, according to Shipping Minister Theodoros Dritsas.
Dritsas said that there are also plan to move migrants away from the former airport at Elliniko, where there has been overcrowding and fights.