The blackout, the cause of which was not immediately known, did not affect traffic control towers and so flights were able to take off and land, Ansa reported, citing officials.
The power cut comes just a day after a fire broke out in the nearby Focene pine grove, forcing the airport to temporarily suspend flights after strong winds blew thick smoke across the runways.
Passengers were still experiencing disruption on Thursday morning, with some flight delays of up to three hours, Ansa said.
A probe was opened on Wednesday as authorities believe the fire might have been started deliberately.
The airport is still struggling to recover from a nighttime blaze triggered by an electrical fault in a bar which sparked scenes of total chaos in early May, with thousands of people hit by flight cancellations and airport staff forced to wear protective masks.
Terminal three, which handles international flights, was seriously damaged and the airport was forced to reduce capacity by 40 percent.