They said the violence, apparently between groups of Syrians and Afghans, erupted in the town of Vathy late on Monday.
A fire later broke out outside the camp that authorities managed to place under control early on Tuesday morning.
"Half of the 6,000 people who are stuck in Vathy camp on Samos are women and kiddies," medical charity MSF said in a tweet.
"This nightmare must end! Children and other vulnerable people must be evacuated from the Greek islands to safe accommodation."
Despite efforts to relocate people to the Greek mainland, there are over 32,000
...the occupiers of Greek Asia Minor..., most of them vastly overcrowded, unhygienic and violence-prone.