The attack took place at 15:50 Ukraine time, news outlets reported.
As a result, fire broke out and is raging inside the shopping mall.
At least two people have been confirmed dead, and 20 injured, according to the deputy head of the office of President Volodymyr Zelensky.
Zelensky himself estimated that 1,000 people had been in the shopping centre at the time of the attack.
The number of victims is expected to increase notably, officials told reporters.
Kremenchuk, situated in the Poltava region, on the Dnieper river, is one of Ukraine’s largest industrial cities.
Monday is day 124 of the Russian invasion of Ukraine.
Source: PAP, Reuters, bbc.com