There was no immediate comment from Russia, which said earlier that it had destroyed six drones in the Black Sea. The Kremlin declined to comment.
"The Ukrainian Armed Forces, together with the Defence Ministry's intelligence unit, destroyed the Tsezar Kunikov large landing ship. It was in Ukraine's territorial waters near Alupka at the time of the hit," the military said on Telegram messenger on Wednesday.
As Russia's war in Ukraine enters its second year, the Black Sea peninsula remains a battleground. (AP PHOTO)
The Black Sea resort town of Alupka lies not far from Yalta on the southern edge of Crimea, which Russian forces seized and annexed from Ukraine in 2014.
Ukraine's GUR military intelligence agency said the warship appeared to have been loaded when it sank and that, before the attack, it had spent some 10 days at a loading site used by the Russian military.
It published grainy footage on Telegram purporting to show several naval drones approaching a large vessel at night and at least one large explosion.
Reuters was able to verify the ship in the video as the Russian Black Sea Fleet's Tsezar Kunikov based on its main mast, antenna, bridge and deck. The location and date the footage was filmed could not be independently verified.
Some of the footage at the end appeared to show major damage with the vessel listing heavily to one side.
"In summary, Tsezar Kunikov received a critical breach on the port side and started sinking," the GUR agency said in a statement.
Kyiv is targeting the Crimea peninsula and taking the two year war beyond Ukraine's borders. (AP PHOTO)
The Project 775 warship, one of Russia's newest vessels, has a crew of 87 and took part in wars in Georgia, Syria and Ukraine, GUR said in its statement.
A Ukrainian news outlet published several videos showing a column of smoke rising over the sea off the southern coast of Crimea with helicopters flying overhead.
Ukraine has used uncrewed navy drones packed with explosives to attack Russian warships to try to drive them out of parts of the Black Sea, making it possible for Ukraine to open a shipping corridor along a traditionally key export route.
Ukraine has no large naval ships left and deliberately scuttled its own flagship at the beginning of the Russian full-scale invasion to prevent it falling into Russian hands.
Newly developed naval drones have been vital for Ukraine as it tries to narrow the vast gap in its naval capabilities with Russia which has a powerful Black Sea Fleet that Kyiv has been trying to degrade.
A senior US State Department official said the use of drones was "an asymmetrical way to rebalance the security picture in the Black Sea" and was helping grow Ukraine's economy to sustain the war effort.
"The fact that the Russian navy cannot operate in the Black Sea at will, compared to how it could operate at the beginning of this war, is a fundamental shift in the strategic position in the Black Sea region," the official told reporters, requesting anonymity.
A senior Ukrainian security official said in December that it had already destroyed 20 per cent of the Russian Black Sea Fleet. Ukrainian Navy spokesman Dmytro Pletenchuk said that Russia had five remaining large landing ships in the Black Sea.
The Ukrainian military says that it has "destroyed" 25 Russian military vessels and ships and one submarine during the war to date. Last month, Ukrainian cruise missiles struck another large Russian landing warship in Crimea.
