"We can confirm that an incident has occurred at Shannon Airport involving a Boeing 763 aircraft. Emergency services are in attendance. All passengers and crew have disembarked. Airport operations temporarily suspended. More information to follow," the airport said.
The Irish Times newspaper reported that the plane was about to depart but returned to the terminal as traffic controllers noticed smoke coming from the aircraft and alerted the flight crew.
Passengers and crew left the plane through emergency slides.
According to reports, Omni Air International is a civilian airline that transports US and foreign military troops the world.
About 300 US troops typically passed through Shannon Airport each day in the first three months of this year, according to Ireland's Transport Ministry.