Washington is also warning Americans not to visit Cuba because some attacks occurred in hotels.
At least 21 embassy staff reported health problems ranging from mild brain trauma and deafness to dizziness and nausea.
Describing the US decision as “hasty”, Cuba said it would affect bilateral ties but co-operation would continue.
Secretary of State Rex Tillerson said the two countries would continue to co-operate in investigating the attacks and said diplomatic ties would be maintained.
Earlier reports suggested that sonic attacks were to blame, but Cuba denies any involvement.
At least two Canadians were also affected.
The US is ordering all non-essential staff in the embassy in Havana to leave, along with all family members. Only “emergency personnel” will remain.
The US has suspended visa processing in Cuba indefinitely.
A US state department official said: “Until the government of Cuba can ensure safety of our people, we will be reduced to emergency personnel.”
“At least 21 employees have been targeted in specific attacks,” the official said.
Despite an investigation involving the FBI, the Royal Canadian Mounted Police and the Cuban authorities, there is still no full explanation as to the cause of the incidents since late 2016.
Earlier reports suggested there were sonic attacks in which staff in Havana were targeted by audio waves, leaving several with chronic hearing issues.
Using an inaudible sound device for a stealth attack “is quite plausible from a technical point of view”, Denis Bedat, a specialist in bio-electromagnetics, told AFP this week.
“Ultrasonic waves, beyond the acoustic capacity of humans, can be broadcast with an amplifier, and the device does not need to be large, or used inside or outside a house.”
He gave as an example the Active Denial System (ADS), an anti-riot gun used by US police forces that emits electromagnetic waves which produce a sudden unbearable burning sensation.
The US has not blamed Cuba for the suspected attacks.
According to the state department official, both the US and Cuban governments “have not yet identified the guilty party”.
“We have not ruled out the possibility of a third country as a part of the investigation but that investigation continues,” he added.
Cuban President Raul Castro had reportedly given his personal assurance to the then-US charge d’affaires in Havana that Cuba was not behind the attacks.
The US reopened its embassy in Havana in 2015 following decades of frozen relations.
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