Jose Carreira, executive director of the European Asylum Support Office (EASO), said at least four shipping containers where interviews were conducted were entirely destroyed, and three more were damaged.
"Incidents have occurred in the past but this is the most serious one," Carreira told AFP.
"We are looking into ways of guaranteeing that this might not happen again," said Carreira, who is in Athens for meetings with Greece's immigration ministry.
No-one was hurt in the incident as the blaze was quickly brought under control by firefighters, but Carreira said it could be days before asylum interviews can resume.
Also Read
The incident took place at the overcrowded Moria camp, one of five centres on Greek Aegean islands, which have borne the brunt of Europe's migrant crisis.
More than 15,000 migrants are being held on the Aegean islands, pending their return to Turkey under an EU-Turkish agreement reached in March this year.
Processing has been held up because the vast majority have filed for political asylum.
Part of Moria, which has a capacity for 3,500 people but currently houses more than 5,000, was badly damaged in a fire during clashes last month between migrants and police.
In Bulgaria meanwhile, some 300 Afghan migrants today protested in the country's largest migrant reception centre, near the Turkish border, according to a human rights group.
"They protested against the fact that they are being kept in Bulgaria against their will and demanded to be able to leave towards Serbia and then (western) Europe," said Iliana Savova, a spokeswoman for the Bulgarian Helsinki Committee for Human Rights, adding that around 300 migrants took part in the demonstration.
Bulgaria's interior ministry confirmed "tensions" at the site, which is home to around 3,800 migrants -- around half of whom are Afghans.
And close to 50 migrants ended a brief hunger strike today in an immigration detention centre in Barcelona, police said, just days after a riot took place in a similar facility in Madrid.
Disclaimer: No Business Standard Journalist was involved in creation of this content