No injuries or major damage were reported.
Authorities said the fire started in some abandoned buildings inside the camp and had been brought under control, NewsChainOnline reported.
The evacuation of the 550 migrants to an empty plot near the camp’s entrance was under way.
Ten unaccompanied minors were to be moved overnight to a new facility on the island.
The transfer of all the migrants to the new 43 million euro facility had been scheduled to begin on Monday and be completed by Wednesday.
The existing camp once housed up to 7,500 migrants in squalid conditions, as Migration and Asylum Minister Notis Mitarakis admitted on Saturday when he opened the new camp.
Originally built to accommodate less than 700 people, Vathy sheltered up to 7,000 asylum-seekers at one point, often drawing criticism from human rights activists.
The new $50 million 12,000-square-meter “closed-style” facility was inaugurated this weekend. It features a double barbed-wire fence, surveillance cameras, X-ray scanners and magnetic doors, as well as a detention center for rejected asylum seekers.
Almost exactly a year ago, a fire ripped through the Moria migrant camp on the Greek island of Lesbos, devouring tents housing around 13,000 people. Greek investigators believe that the fire was deliberately started by the asylum-seekers themselves in protest against Covid-19 restrictions.