It was not immediately clear what had happened, but spokeswoman Heather Nauert said there were no “definitive answers about the source or cause”.
One government official quoted by Reuters said that some staff had suffered hearing loss.
Cuba’s foreign ministry announced it was investigating the allegations.
Cuba called the expulsion of its staff unjustified but said it was willing to co-operate with Washington to clarify what had happened.
The ministry said: “Cuba has never, nor would ever, allow the Cuban territory to be used for any kind of action against accredited diplomats or their families.”
It was suggested the hearing loss could have been caused by some kind of sonic device placed outside the diplomats’ homes, emitting inaudible sound waves that can cause deafness.
Heather Nauert said staff began complaining of the strange symptoms late last year.
While they were not life-threatening, she revealed that a number of people had been brought home to the US as a result.
Heather Nauert said the government was taking it “very seriously, and there is an investigation currently under way”.
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The US and Cuba only re-established ties in 2015, following 50 years of hostilities between the two countries.
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