Thousands of migrants are reportedly homeless around the Greek island of Lesbos after fleeing fires that gutted their camp, as a result, authorities are worried that some asylum seekers who tested positive for COVID-19 could spread the virus.

A senior Greek official told Reuters that the Moria camp, which hosts more than 12,000 people, was "probably totally destroyed".

According to the official, the fire broke out just after midnight and by dawn on Wednesday, most of the camp was on fire, with a few people searching through the debris for their possessions.

It is not clear what caused the fire but authorities are investigating whether they were started deliberately.

Upon the tragic incidence, however, Athens declared a state of emergency on Lesbos and sent police reinforcements to the island, off Turkey, to help keep order.

About 3,000 migrants and refugees would be temporarily housed in tents as the government mulls ways to provide shelter for the displaced citizens, Deputy Migration Minister George Koumoutsakos.

Meanwhile, the whereabouts of 35 migrants who tested positive for COVID-19 this week were unknown. The camp had been placed under quarantine last week after an asylum-seeker tested positive.

Initial reports suggested the fires broke out at different locations in the sprawling camp after authorities tried to isolate some individuals who had tested positive for COVID-19.

The camp which is home to nearly 13,000 people has long received criticism from aid groups. They say it is impossible to implement social distancing and basic hygiene measures there.

A statement issued by UNHCR, the UN refugee agency, said it was aware of "tensions" between nearby citizens and the migrants.

"We urge all to exercise restraint," it said, and asked anyone who had been at the camp "to restrict their movements and stay near [the site], as a temporary solution is being found to shelter them."