Protesting migrants have set fires inside and outside the Moria camp, on the island of Lesvos, demanding to be transferred into the mainland.
The migrants have clashed with police forces, a local website, lesvospost.gr reports.
Fire service officers have reached the site, trying to put the fires out.
Police and local authorities say there are reports of fatalities, but not confirmation.
But UNHCR Greece have tweeted that “we learned with deep sadness that the lives of a woman and a child were lost in a fire on Lesvos today."
The overcrowded camp, built to house 3,000, hosts 12,000 in often squalid conditions. Flows of migrants coming to Greece have increased substantially recently, although they are not yet at the historically high 2015 levels, when more than 800,000 entered the country.