Cuba has denied involvement in any attacks and says it has reinforced security for US diplomatic personnel.
Secretary of State Rex Tillerson said then that USA tourists should avoid the island altogether.
Cuba has denied involvement in the attacks.
A mysterious illness that sickened US diplomats in Cuba reportedly has also affected American travelers who stayed at two hotels in Havana.
The steps being taken by President Donald Trump's administration mark a further blow to his predecessor Barack Obama's policy of rapprochement between Washington and Havana, former Cold War foes.
A State Department spokesperson, who declined to be named, said the agency could not verify the claims but said travelers should heed its travel warning issued last Friday.
The State Department warned on its website last week that American citizens should avoid travel to Cuba because of the identified source of "attacks" on embassy employees and concerns that "U.S. citizens may also be at risk". A news release said the department "imposed limitations" on two hotels, where the so-called acoustic attacks have taken place: Hotel Nacional and Hotel Capri.
Chemist says VX byproduct was on Kim murder suspect's shirt
The nerve agent is banned by an worldwide treaty as a weapon of mass destruction. Its lethality depended on the dosage and where on the body it was applied.
He said he would not lift the USA trade embargo on the Caribbean island until it made "fundamental reforms".
The State Department said Friday that several Americans who don't work for the government have also reported symptoms after traveling to Cuba that were included in the travel warning.
Cuba, the United States and Canada have investigated the attacks, but the probe has not yielded any answers about how they were carried out or who was responsible for them. Typically, in instances where the State Department is concerned a particular site may be unsafe, USA personnel are prohibited from staying there.
"It looks like we are returning the threats and tensions of the 1960s", said Maria Fernandez, a 45-year-old office worker in Havana. "It's really sad, because we are so close, and yet so far away from a honest rapprochement". Cuba described his comments as "unacceptable and meddling".
The Cuban government insists that it has played no role in the attacks and is working USA investigators to determine the cause of these ailments.
In a message on, the embassy's top official, career diplomat Scott Hamilton, said he would also be leaving. "Hasta la proxima Cuba".