The Black Sea port of Odesa, which is key for Ukrainian exports, has faced persistent missile and drone attacks from Russian forces since the beginning of their invasion in February 2022.
"Russian occupants attacked the Odesa region with two cruise missiles. One of them was eliminated," the air force said on social media.
The military acknowledged that a warehouse had been hit in the attack and that three men had been wounded, without elaborating.
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AFP journalists in Odesa saw large columns of smoke rising over a charred building.
The region's governor said the blaze had spread over 3,000 square metres (3,590 square yards).
"Rescuers are now working to prevent the fire from spreading to the entire building," governor Oleg Kiper said on state television.
East Ukraine has borne the brunt of more than two years of fighting, but the south of the country has also been targeted in regular strikes from Russian forces.
Guided aerial bombs hit Ukrainian-controlled areas of the southern region of Kherson, its governor said on Monday.
"A 40-year-old man, who was on a balcony at the time of the bombardment, sustained fatal injuries," governor Oleksandr Prokudin said, adding the attacks wounded two other people.
In the northeastern region of Kharkiv, the governor said two people were killed when their car hit a Russian anti-tank mine near the border village of Lyptsi.
Lyptsi was targeted last month when Russian forces launched a surprise ground offensive over the border that has forced thousands to evacuate.
EXPLAINED: What We Know About Russia’s Oreshnik Missile Fired on Ukraine
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