As many as 78 flights by the country's largest carrier Cebu Pacific were cancelled, affecting nearly 14,000 passengers, the company said in a statement.
Flag carrier Philippine Airlines also said some of its flights were cancelled or delayed but could not immediately say how many.
The blackout hit Terminal 3, which services mostly domestic flights, late yesterday and power was not restored until before dawn today.
Exhausted passengers sprawled on the floor as check-in counters and luggage carousels shut down. Long queues formed outside the terminal as entrances were closed until power was restored.
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It is one of four terminals in a complex that was once dubbed by the travel website Guide to Sleeping in Airports as the world's worst due to leaking toilets and creaking facilities.
"We are looking into the root cause of this problem," Terminal 3 general manager Octavio Lina told DZMM radio.
Manila power retailer Meralco said a transmission line tripped briefly but was restored in minutes, suggesting that the problem could be with the airport's systems.
Plans to build a new airport outside Manila have not materialised under Aquino. An excruciatingly slow infrastructure overhaul has led to chronic commuter train breakdowns and traffic jams.