Footage posed by public broadcaster Suspilne on the Telegram messaging app showed rescue workers sifting through large piles of rubble, burning wreckage and a large crater in what it said was Shevchenkove, southeast of the regional capital Kharkiv.
Oleh Synehubov, governor of the Kharkiv region, wrote on Telegram that "unfortunately a 60-year-old woman died".
"All other victims were hospitalised. Doctors are helping them. Rescue workers continue to clear the debris," he said.
He had said earlier that at least seven people were wounded, including a 13-year-old girl.
Andriy Yermak, head of the presidential administration, also said one person had been killed and posted a photograph of the market in flames on Telegram.
Criticising Russia over the attack, he wrote: "Common terrorists."
The reports and images of the attack could not immediately be verified independently by Reuters.
Suspilne quoted a local official as saying at least three pavilions were destroyed in the attack and that a shopping centre was damaged, but that Monday was not a market day.
Russia, which invaded Ukraine more than 10 months ago, did not immediately comment on the reported attack.
(Reporting by Pavel Polityuk, Editing by Timothy Heritage)
