Police say shots were fired in the terminal's check-in area on Sunday afternoon local time. No-one was reported injured.
The man was quickly detained, and a firearm recovered. His motives remain unclear.
The capital's airport was evacuated as a precaution.
Australian media report that the gunman fired approximately five shots. Bullet holes were later seen in the glass windows of the terminal.
Footage has emerged on social media purportedly showing a man being arrested by police officers at the airport.