He posted a picture of firefighters next to a charred car.
Oleksandr Prokudin, the head of Kherson’s regional military administration, said the casualties occurred when a car was hit by a shell and caught fire.
The strike came two days after Russian artillery fire also killed three people in Kherson, according to the Ukrainian presidency.
Kherson is the capital of one of the four regions — along with Donetsk, Lugansk and Zaporizhzhia — that Russia claims to have annexed but does not fully control.
Despite Russia’s retreat from the city of Kherson late last year, it has been regularly pounded by Moscow’s troops.
Several cars were damaged as a result of the shelling.
Galyna Kolisnyk, 53, said the Russians struck when she was in a store.
“When we entered, literally five minutes later this tragedy happened,” she told AFP.
“Explosions began, our car got hit….This is horrible.”