Flights were suspended for 90 minutes. The airport said it "regrets any inconvenience to passengers".
It said "knock-on delays" were likely and has advised passengers to check with their airline for flight information.
The Dublin Airport Authority said the fire was in a restricted area, separate from the passenger facilities. There are no reports of any injuries.
A number of flights were diverted to Belfast City and Shannon airports.
Passenger Denny Murray said he saw the fire-fighting effort as he arrived at the airport.
"We were on the motorway and could see the fire brigade as we approached," he said.
"We didn`t see flames but we saw jets of water being aimed at the building. Everything seems to be pretty normal, except all the screens say there`ll be more information in ten minutes."
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