The ministry also released grainy over-head footage on social media showing in black and white what appeared to be an explosion over a light craft with debris spilling outwards.
"Ukrainian Bayraktar TB2 destroyed another Russian ship. This time the landing craft of the "Serna" project. The traditional parade of the Russian Black Sea fleet on May 9 this year will be held near Snake Island - at the bottom of the sea," it said in a tweet.
The military said in a separate statement on social media that the Bayraktar drone strike had also destroyed Tor-M2 anti-aircraft system being delivered to the island.
Western military analysts said a Ukrainian counteroffensive was advancing around the country's second-largest city, Kharkiv, even as it remained a key target of Russian shelling.
Ukraine earlier this month said its drones destroyed two Russian patrol boats, also near Snake Island.
Meanwhile, six Russian cruise missiles fired from aircraft hit Odesa, where a curfew is in place until Tuesday morning. Videos posted on social media showed thick black smoke rising over the Black Sea port city as sirens wailed.
The Odesa city council said four of the missiles hit a furniture company, with the shock waves and debris badly damaging high-rise apartment buildings. The other two missiles hit the Odesa airport, where the runway had already been taken out in a previous Russian attack.
In Mariupol, Ukrainian fighters made a final stand against a complete Russian takeover of the strategically important city, which would give Moscow a land bridge to the Crimean Peninsula, annexed from Ukraine during a 2014 invasion.
The largest European conflict since World War II has developed into a punishing war of attrition that has killed thousands of people, forced millions to flee their homes and destroyed large swaths of some cities.
