According to the Irish Sun newspaper, the note was found in the toilet of the aircraft.
"The passengers have disembarked, and the plane and passengers are in the process of being searched," the Irish police said.
The plane had 214 passengers and the crew on board safely landed at Shannon Airport, after which the passengers and their luggage went through a screening over the security concerns.
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The United Airlines said it canceled the flight and was working to provide the passengers with refreshments and overnight accommodation.
The flight is scheduled to depart Shannon Tuesday afternoon local time.