The strike appears to form part of an aggressive new Russian strategy.
Over the past three days its missiles have hit several civilian sites lying hundreds of miles from Ukraine’s main battlegrounds, including an apartment block in Kyiv.
Volodymyr Zelensky, the Ukrainian president, said that there were “a thousand people” in the Amstor shopping mall in Kremenchuk, when the missile struck in the middle of the afternoon.
“The mall is on fire, firefighters are trying to extinguish the fire, the number of victims is impossible to imagine,” he said.
Videos on Twitter showed flames and black smoke billowing out of the shopping mall and civilians helping overwhelmed emergency crews load people into ambulances.
A fire engine donated by Humberside Fire and Rescue in England doused the flames.
In one video, shot from inside the shopping mall, a man steps over broken glass and rubble to escape a smoke-filled room. For one moment, the camera pans across a small motionless body.
Dmitry Lunin, the mayor of Kremenchuk, said that at least 10 people had been killed in the attack and 40 injured but that these numbers were expected to climb.
“In Kremenchuk a civilian target was hit and there are civilian deaths, unfortunately,” he said.
Kremenchuk is an important industrial city of around 220,000 people lying on the Dnieper River.
It is the base for a truck plant, an oil refinery, a railway carriage plant and a hydroelectric dam. Russian missiles have hit the oil refinery three times previously, destroying it. The most recent attack was in mid-June.
British Prime Minister Boris Johnson, who was attending the G7 summit in Bavaria, Germany, which has been dominated by talks on how to support Ukraine, said that the attack should strengthen the West’s resolve.
“This appalling attack has shown once again the depths of cruelty and barbarism to which the Russian leader will sink,” he said.
In the past three days Russia has fired missiles at what it has described as legitimate logistics targets in Ukraine.
On Saturday it hit Ukrainian army training centres around Kyiv and on Sunday it fired cruise missiles at several other sites hundreds of miles from the Kharkiv and Donbas battlegrounds.
The Russian ministry of defence has said that it targets infrastructure with high-precision missiles but it has also destroyed an apartment block in central Kyiv for the first time since April.
At least two people were killed in the attacks.
Russian President Putin had promised to strike “new targets” after Britain and the US pledged to send new long-range missile systems to Ukraine earlier in June, but Russia has been accused of targeting civilians to undermine morale.
In Donbas, Russian officials said that street battles were being fought in Lysychansk after Russian soldiers completed their conquest of the town of Severodonetsk over the weekend.
“Russians are storming Lysychansk and occupied Severodonetsk awaits a humanitarian disaster,” Serhiy Haidai, the Ukrainian governor of the Luhansk region, wrote on Facebook.
Russian forces have trucked in food and medicine for the estimated 10,000 people who remained in Severodonetsk throughout the battle but Mr Haidai said that this was not sufficient.
Lysychansk is the last town in the Luhansk region that is not under the control of Russian forces.
Telegraph Media Group Limited