A photograph showed a plume of smoke blocking out sunlight over the city.
Five people were killed in the Russian attack on port infrastructure, according to a report by Ukrainska Pravda, citing Dmitry Pletenchuk, a Ukrainian naval spokesman.
Sirens sounded across the wider Odesa region at 10.41am local time, with the explosion rocking the city shortly after. Ukraine’s air force declared a ballistic missile warning four minutes later.
It was not clear whether the attack was aimed at Mr Zelensky, who was visiting the port in Odesa at the time.
The Ukrainian president’s aides did not immediately respond to questions over the strike.
Mr Zelensky has been subjected to at least a dozen failed assassination attempts since the start of the Russian invasion in February 2022, according to Mikhail Podolyak, his senior adviser.
Russia has not shied away from attacking major Ukrainian cities while overseas dignitaries are visiting.
Notably, a barrage of Russian missiles were aimed at Kyiv as a delegation of African leaders arrived in the capital in the hope of brokering peace talks between Russia and Ukraine.
Earlier this month, Annalena Baerbock, the German foreign minister, cut her visit to the Ukrainian capital short after she was trailed by a Russian drone.
Ursula von der Leyen, the European Commission’s president, condemned the latest strike as “vile”.
“No one is intimidated by this new attempt at terror – certainly not the two leaders on the ground nor the brave people of Ukraine,” she wrote on X, formerly known as Twitter.
Odesa is considered symbolic for Athens after waves of Greeks arrived in the city in the eighteenth century. The Society of Friends, a revolutionary movement, which aimed to free Greece from the Ottoman empire, was later founded there.
Mr Mitsotakis, who has pledged to help rebuild the city, described it as a “vital hub of Hellenism on the shores of the Black Sea”.
Russia later claimed it had hit a hangar housing Ukrainian naval drones. The defence ministry said in a statement: “The goal has been achieved. The target has been hit.”
