In an interview with the BBC, he said hooligans were known to the authorities and security services "will be watching all the matches closely".
His comments follow a BBC documentary which depicted widespread racism at Ukrainian football matches.
On the issue of hooliganism during the Euro 2012 championships Ukraine's President said the problem in Ukraine was probably "smaller" than in other countries.
"We have a list of people who behaved aggressively at football matches. Their numbers are tiny, they are known to us and preventive measures will be taken," he said.
Last week, a BBC Panorama documentary exposed widespread racist and anti-Semitic chanting, Nazi salutes and attacks on minorities at football matches in Ukraine.
After watching the footage, footballer Sol Campbell told fans to "stay at home, watch it on TV. Don't even risk it… because you could end up coming back in a coffin".
Despite the warning from the former England captain, President Yanukovych said his country had "created all the infrastructure for football fans to feel good and for Ukraine to show all its capabilities".
"We are waiting for our guests with great pleasure," he said.
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