An airport spokesman said the man and a woman were late for a Ryanair flight to Amsterdam on Thursday morning.
Talking to staff at the boarding gate, the man reportedly became agitated when he was told he would not be able to board the flight, broke through the door and began running towards the plane.
One witness inside the airport, Declan Harvey, said he could hear a man shouting “Wait!” as the plane taxied on the apron, before he was tackled to the ground by airport staff.
The flight was momentarily delayed.
A Dublin Airport spokeswoman said the man had become agitated after being told he could not board his flight.
“He was banging on the window to try and get the aircraft to wait and he then broke through a door and made his way on to the apron, trying to flag the aircraft down.
“He was was initially restrained by Ryanair staff on the apron, and airport police, who had already been contacted, arrived on the scene almost immediately and arrested him.
“He was taken to the airport police station and handed over to the gardai.”
Officers confirmed they were called to Dublin Airport at around 7am.
The man will appear at the Criminal Courts of Justice in Dublin on Thursday.