President Volodymyr Zelenskiy said more than 1000 people were in the shopping centre at the time of the attack, which witnesses said caused a huge fire and sent dark smoke billowing into the sky.
A Reuters reporter saw the charred husk of a shopping complex with a caved-in roof.
Firefighters and soldiers were pulling out mangled pieces of metal as they searched for survivors.
"It is impossible to even imagine the number of victims... It's useless to hope for decency and humanity from Russia," Zelenskiy wrote on the Telegram messaging app.
Dmytro Lunin, governor of the central Poltava region, told Reuters that 10 people had been confirmed killed and that rescue workers would keep searching through the smouldering rubble for two days, with more bodies likely to be found.
"It's an act of terrorism against civilians," he said separately, suggesting there was no military target nearby that Russia could have been aiming at.
At one point, paramedics rushed into the building after rescuers called out "200" meaning they had found one or more bodies in the building.
Reporters were later pushed away from the scene as air raid sirens wailed again.
Kremenchuk, an industrial city of 217,000 before Russia's February 24 invasion of Ukraine, lies on the Dnipro river in the region of Poltava and is the site of Ukraine's biggest oil refinery.
Ukraine's air force command said the mall was hit by two long-range X-22 missiles fired from Tu-22M3 bombers that flew from Shaykovka airfield in Russia's Kaluga region.
Russia did not immediately comment on the Ukrainian assertion.
It has denied deliberately targeting civilians during in its "special military operation" in Ukraine.
"We need more weapons to protect our people, we need missile defences," Andriy Yermak, head of the president's office, said.
Vadym Denysenko, an interior ministry adviser, said Russia could have had three motives for the attack.
"The first, undoubtedly, is to sow panic, the second is to... destroy our infrastructure, and the third is to... raise the stakes to get the civilised West to sit down again at the table for talks," he said.
Russia, which has captured the eastern Ukrainian city of Sievierodonetsk after a weeks-long assault, has stepped up missile strikes across Ukraine in recent days.
Missiles hit an apartment block and landed close to a kindergarten in the Ukrainian capital on Sunday, killing one person and wounding several more people.
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