In announcing the move, Secretary of State Rex Tillerson said Washington would maintain relations with Havana -- which were only fully restored in 2015, and which have deteriorated since President Donald Trump took office in January.
"Cuba has told us it will continue to investigate these attacks and we will continue to cooperate with them in this effort," Tillerson said in a statement.
"We maintain diplomatic relations with Cuba, and our work in Cuba continues to be guided by the national security and foreign policy interests of the United States."
The attacks of an unknown nature have targeted at least 21 US embassy staff in Havana over the past few months, Tillerson said.
Those affected have exhibited physical symptoms including ear complaints, hearing loss, dizziness, headache, fatigue, cognitive issues, and difficulty sleeping, he added.
"The health, safety, and well-being of our embassy community is our greatest concern. We will continue to aggressively investigate these attacks until the matter is resolved," Tillerson said.
Routine visa operations will be suspended indefinitely in response to the attacks, a senior State Department official said.
Cuba reacted by calling the US move hasty, and said it would affect bilateral relations.
Still, Cuba wants to work with the United States to resolve this case, said the head of North American affairs at Cuba's foreign ministry, Josefina Vidal, quoted on state television.
"The Cuban government has no responsibility in this case and strictly respects its obligations under the Vienna Convention" governing the protection of diplomats as well as their families, she added.
'No definitive answer'
US officials had previously told reporters they believed some kind of inaudible sound weapon was used on American staff either inside or outside their residences in Havana.
Canadians in Cuba have also been impacted, with a source close to that country's embassy telling AFP that more than five families were affected, including several children.
US suspicions were first aroused in late 2016, but Washington waited until August 2017 to announce that several of its embassy employees had fallen victim to mystery health problems.
Questions linger over whether they are the result of targeted attacks, sabotage, or an accident.
Washington has not accused Cuba of being behind the incidents, but has repeatedly warned that Havana is responsible for the safety of foreign envoys on its soil.
The US expelled two Cuban diplomats in May and Tillerson has raised the possibility of closing the American mission in Cuba altogether over the issue.
Cuban Foreign Minister Bruno Rodriguez Parrilla said last week the country has found no evidence to support US claims that diplomats were harmed due to attacks.
It is unclear who would have carried out such an attack, and for what ends.
Numerous observers doubt that Cuba would have risked antagonizing its neighbors at the end of 2016 -- when relations between the former Cold War enemies were thawing, before they deteriorated under Trump.
Likewise with Canada, the biggest source of big-spending tourists to Cuba. According to Canadian diplomats, Ottawa does not suspect senior Cuban officials of involvement.
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Accidental?
Rumors are rife on both sides of the Florida Strait, including of a plot by rogue Cuban agents aiming to derail rapprochement with Washington.
Others suspect a third country with the same aims, such as Russia or North Korea.
The most common hypothesis is that the health issues may be purely accidental, an unfortunate consequence of defective and outdated listening systems -- a theory reinforced by Cuba's reputation for having "big ears."
Several experts undermine that view however, saying eavesdropping systems are typically receptors, and not emitters, of signals. And, according to US media, investigators have turned up nothing suspicious in meticulous searches of the victims' residences.
Senator Marco Rubio, a son of Cuban immigrants and outspoken critic of the Havana government, said that until those responsible for the attacks are found, the United States should expel from Washington the same number of Cuban diplomats as Americans it is pulling from Havana.
Washington should also consider putting Cuba back on a terror blacklist, Rubio said.
