Video footage, posted on Twitter by the BBC's Greece correspondent, showed a young man holding a petrol can and addressing camp residents, and then catching fire as a policeman approached.
The unidentified man was rushed to hospital with burns over 90 per cent of his body, ANA said. The policeman who tried to save him was also hospitalised with burns.
Thousands of people, many of them Syrians fleeing war, are stuck in Greece's Aegean islands as a result of an EU-Turkish agreement that curbed the influx of migrants to the European Union.
In a separate incident, Greek police said today they had arrested a people trafficker who imprisoned 23 South Asian migrants for a week in a bid to blackmail their families into paying money for smuggling them into Greece.
The 26-year-old Greek national was demanding between 1,500 and 3,000 euros (USD 1,600 to USD 3,200) a head. The migrants had only made an up-front payment.
Police were alerted by a migrant who complained that his brother and a nephew were being held in the warehouse in Menemeni, a small town near the northern city of Thessaloniki, a police statement said.
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