There were no reports of injuries after the fire started in the early hours of Wednesday at Moria camp.
The cause of the blaze which burned tents and containers was not immediately clear, a fire brigade official said.
A police official said that migrants had been taken to safety. People were seen leaving the camp, carrying their luggage, witnesses said.
At least 25 firefighters with 10 engines, aided by police, were battling the flames both inside and outside the facility, the fire brigade said, adding that emergency personnel were pushed back by migrants during their efforts to put out the fire.
The Moria facility, which hosts more than 12,000 people – more than four times its stated capacity – has been frequently criticised by aid groups for poor living conditions.
It was placed under quarantine last week after authorities confirmed that an asylum-seeker had tested positive for the coronavirus. Confirmed infectionshave risen to 35 since then.
Lesbos, which lies just off the Turkish coast, was on the front line of a massive movement of refugees and migrants to Europe in 2015-2016. Due to the coronavirus pandemic, since 1 March, all migrants reaching the island have been quarantined away from the camps.
In Moria, aid groups have warned that social distancing and basic hygiene measures are impossible to implement due to the living conditions.
A child died after a fire at the camp in March.
Wildfires fanned by strong winds were also burning in two other areas on the island.
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