The makeshift camp is located at the abandoned old Athens airport and houses more than 3,000 migrants, including many children.
In this latest outbreak of violence at refugee camps in Greece, it was reported that the fight involved some 50 other refugees, mostly Afghans, according to the AP.
The man was said to be around 20-years-old. He was seriously injured in the brawl and then transferred to a local hospital where he then succumbed to his injuries and died.
Police reinforcements were sent to the camp and two other migrants of unconfirmed nationalities were also hospitalized with injuries.
Tension has been rising as more and more migrants are arriving in Greece and having to live in the already overcrowded camps as a final decision of whether or not their asylum will be granted is debated.
The total number of migrants and refugees stranded in camps in Greece as of July topped around 57,000.