The southern operational command claimed it had caused major losses to Russian troops after it "aimed strikes with the use of various forces" on the island.
Damage inflicted by Ukrainian forces could be seen on satellite images, with a tower and vegetation destroyed. Russian vehicles, a radar station and a Pantsir anti-aircraft system were also damaged.
The strategic island, which sits 80km off Ukraine’s southern coast, was seized by Russian forces early on in the war. It has become the site of numerous bombing raids.
Snake Island became a symbol of Ukrainian resistance after an expletive-ridden radio exchange went viral at the start of the war, in which defenders refused demands from the Russian warship Moskva to surrender.
Roman Hrybov, a Ukrainian border guard, radioed "Russian warship, go f— yourself" to Russian soldiers on board the ship.
It was thought that Hrybov and his crew had died during the attack, but last month they returned to Ukraine in a prisoner swap.
The latest success by Ukrainian forces will come as yet another blow to the Kremlin, which is also thought to have lost 55 per cent of its pro-Russian separatists in Donetsk, according to British intelligence.
It comes just days after a Russian ship delivering armaments and crew was destroyed by two Harpoon missiles.
According to Ukraine, it marked the first time the country’s forces had hit a Russian vessel with the Western-supplied anti-ship rockets.
Sources said 10 of the 33 crew members were killed and the remaining injured.
Harpoon weapons were sent to Ukraine by the United States, while the UK and Denmark are considering following their lead.
Russia claimed on Wednesday that it had repelled a "mad attack" by Ukrainian forces that saw their forces "plan to carry out massive air and artillery fire... before landing and capturing" Snake Island.
"On June 20 at 5:00 am, the Kyiv regime undertook another mad attempt to take possession of Snake Island," Russia's defence ministry said in a briefing.
The ministry said 15 Ukrainian attack and reconnaissance drones took part in the airstrike, while missile launchers and howitzers fired at the island, with 13 drones reportedly shot down.
It also said that Russian radars had detected a US RQ-4 "Global Hawk" reconnaissance drone in the area.