In a statement, Ukraine’s foreign ministry said the move would undermine the image of the tournament and be detrimental to millions of Ukrainians and Poles.
Poland – which is co-hosting Euro 2012 – has also criticized any boycott.
Several European leaders are considering cancelling their trips to Ukraine, in protest over the treatment of jailed former PM Yulia Tymoshenko.
Yulia Tymoshenko, who is on hunger strike, alleges she was beaten by prison guards.
The statement from the Ukrainian foreign ministry said sport events were designed to bring unity, and criticized what it said were attempts to politicize them.
“We view as destructive attempts to politicize sporting events, which since ancient times have played a paramount role in improving understanding and agreement between nations,” the statement said.
“A successful championship will be a victory not for politicians, parties or ideologies, but for all Ukrainians and Poles. Its failure will be a loss for millions,” it said.
Austria has said it will boycott all the matches in Ukraine, while the Netherlands said it will not attend unless Yulia Tymoshenko’s treatment improves.
On Thursday, EU officials said European Commissioner Jose Manuel Barroso would not be attending.
German Chancellor Angela Merkel is also reported to be considering boycotting the event, while the UK says it is undecided on whether to attend.
Meanwhile, five European presidents – from Austria, the Czech Republic, Germany, Italy and Slovenia – have said they will not attend a Ukrainian summit of Central and East European leaders next week in Yalta.
In an attempt to ratchet up the pressure further, Germany earlier said the EU is prepared to delay a trade agreement with Ukraine.
German Foreign Minister Guido Westerwelle said that “with our EU partners we are unanimous that the EU Association Agreement with Ukraine cannot be ratified as long as the rule of law in Ukraine does not develop in the right direction”.
But Ukraine’s deputy prime minister has said Euro 2012 is on track and UEFA – European football’s governing body – had not complained.
“The tournament is ready and on 11 May we will be transferring the control of the four stadia to UEFA.”
Yulia Tymoshenko, a former prime minister, was jailed last year for abuse of office, in a trial condemned by the West as politically motivated.
She is an arch-rival of Ukraine’s President Viktor Yanukovych, who beat her to the presidency in February 2010, avenging his defeat in the 2004 Orange Revolution.
The opening games of the month-long Euro 2012 will be played on 9 June.
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