The envelope, which was received at Joint Base Myer-Henderson Hall around 3:30 pm (2030 GMT), led to an evacuation of the building, the US Marine Corps said in a statement.
"Shortly after receiving the letter, 11 people started to feel ill," three of whom were "transported in stable condition for further medical evaluations," it said.
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"Joint Base Police Department officials are working with local HAZMAT teams, NCIS (Naval Criminal Investigation Service) and the FBI. The building was screened and cleared," it said.
CNN reported that a corporal, gunnery sergeant and a colonel complained of a "burning sensation" on their hands and face.
Marine spokesperson Major Brian Block said it was too soon to say whether the incident was being considered a terror attack.
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"It's way too early to start speculating on any of that, we have to wait and let the investigators do their jobs," Block told AFP.
Joint Base Myer-Henderson Hall overlooks Arlington Cemetery just across the Potomac River from Washington.
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