The reporting follows several explosions on the island, which is situated on the Strait of Hormuz, according to state media outlet IRNA.
The attack on Monday was the latest in a series of limited strikes carried out by Washington in recent weeks, the Wall Street Journal said.
It added that strikes had been carried out on a smaller scale and purposefully kept secret so as not to signal any intent of resuming its major military campaign against Iran.
The US Central Command did not immediately respond to a request for comment.
Earlier on Monday, US President Donald Trump raised doubts about whether he would follow through on a threatened resumption of military strikes against Iran and said a deal with Tehran could happen.
Asked by reporters if he was considering striking Iran after Tuesday's midterm elections, Trump replied "no".
Washington and Tehran have been at war since February 28 but Trump is under pressure to settle the conflict which has sent fuel prices soaring.
Earlier, officials in Tehran said contact between Iran and the US to end the war were continuing after days of Iranian talks with Qatari mediators ended with altered proposals but no breakthrough.
"Consultations through mediators are very intensive. We have presented our conditions and proposals and everything depends on the political rationality of Washington," Iranian Foreign Minister Abbas Araqchi said in comments carried by state media outlet IRNA.
"If the US accepts our conditions, the Strait of Hormuz will be reopened and negotiations will be resumed," he said.
Iranian President Masoud Pezeshkian said the country's supreme leader had granted "certain authorities" to the government in regards to peace talks, state media reported.
with AP
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