The US strike is the first known attack on Iran since President Donald Trump paused a renewed military campaign in late July.
Larak Island is just offshore from the key port of Bandar Abbas and sits right on the Strait of Hormuz, a vital waterway for global shipping.
Iran is currently making tanker traffic pass by this island for checking and reportedly forcing vessels to pay $2m (£1.5m) to cross.
Hossein Mohebbi, the IRGC's spokesman, called the attack a "strategic and fatal mistake by the Trump regime" and said that the "enemy will pay the consequences of this miscalculation in both the economic and military fields".
Iranian President Masoud Pezeshkian said in a statement quoted by state TV: "We are not seeking war, but we will deliver a decisive response to the aggressors," according to AFP.
Iran's Tasnim news agency, which is affiliated with the IRGC, said earlier that the attack was carried out by drones.
Hours later, Iranian media carried a statement by the IRGC saying it had attacked the US bases of King Hussein and al-Azraq in Jordan with ballistic missiles in response to the Larak Island attack.
The IRGC said it had caused "heavy damage" and targeted "technical infrastructure, maintenance facilities, and enemy fighter jet positions", according to a translation from the AFP news agency.
Hours after the strike, Trump posted apparent AI videos on Truth Social showing oil infrastructure exploding.
One was captioned "Kharg Island being blown to smithereens!!!" in reference to a major oil terminal off the coast of Iran which Trump has threatened to take. His post did not elaborate.
Trump said last week that all mines placed in the Strait of Hormuz by Iran as part of its efforts to blockade the route had been detonated or removed. He said Iran had been warned that any ship or boat deploying new mines would be destroyed.
Iran's Deputy Foreign Minister Kazem Gharibabadi described Trump's claim as a "propaganda" deception.
Iran is facing renewed economic pressure after Washington announced a fresh sanctions campaign on 24 August aimed at further isolating Tehran and expanding secondary sanctions against its allies.
Iranian officials and state media have largely dismissed the campaign as a continuation of previous US economic measures, which they argue followed Washington's military failure in the recent conflict.
The US and Israel launched wide-ranging strikes on Iran on 28 February, with Iran responding by attacking Israel, US bases and allied states in the Gulf, and effectively closing the Strait of Hormuz to marine traffic. The Iran war has now crossed its six-month mark.
Some 20% of the world's oil and liquefied natural gas used to travel through before the war began.