The passenger jet touched down safely at 1.37pm, having taken off at 11.15am.
There were reports of smoke being detected on board.
It is believed there were 239 passengers and crew on the aircraft.
A Shannon Airport spokeswoman confirmed the aircraft had been diverted due to a technical problem.
Emergency services attended the scene as a precaution.
A British Airways spokesman said: "The aircraft landed normally after our highly-trained pilots diverted the flight as a precaution."
British Airways said a replacement aircraft was being arranged to take passengers to Boston.