The incident occurred between afternoon showings of the Hollywood movie Armageddon at a local cinema in the western Ukrainian town of Chervonohrad near the Polish border.
A group of children was trying to leave the cinema after a showing of the film, while a stream of others tried to rush through to the next viewing.
One report said the schoolchildren got crushed in a narrow corridor after violent pushing and shoving.
A police officer told Reuters news agency: "The children fell on each other in the mess that formed quickly."
Police say the three boys and a girl who died were aged between 12 and 13. Six others were seriously injured and are under intensive care in hospital.
About 800 children in all had come to watch the thriller, which has been running for several months in Ukraine.
Its star, Bruce Willis, has an avid following in the country.
The Ukrainian President, Leonid Kuchma, offered his condolences and ordered an inquiry.
Reports say that is likely to focus on why the doors of the cinema were opened to incoming children before the others had left.
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