Relations between Ukraine and the European Union have been strained by the conviction of Yulia Tymoshenko - the main political rival of President Viktor Yanukovich - last October, a case her supporters say was politically driven.
A German government spokesman said any visit by Chancellor Angela Merkel during the tournament would be linked to Tymoshenko's fate. Several other leaders also said they would scrap plans to visit Ukraine over the case.
"I would not like to think that German state leaders can reanimate methods of the Cold War period and make sports a hostage of politics," Ukrainian foreign ministry spokesman Oleh Voloshin told Interfax news agency.
Earlier, Czech President Vaclav Klaus joined German President Joachim Gauck in cancelling participation at a summit of central European presidents in the Ukrainian Black Sea resort of Yalta on May 11-12 over Tymoshenko's case.
And in Brussels, a spokeswoman for European Commission President Jose Manuel Barroso said he would not visit Ukraine because of Tymoshenko's treatment.
"As far as the president is concerned, it is clear that as things stand now, the president has no intention of going to Ukraine or indeed participating in events in Ukraine at this point in time," Pia Ahrenkilde Hansen told a briefing.
Tymoshenko, 51, who was jailed for seven years after a court ruled she exceeded her powers as prime minister, is in a prison in the city of Kharkiv - one of the venues of the championship.
Ukraine is co-hosting the Euro-2012 tournament - one of the continent's main sports events - together with Poland, and hopes to improve its image and boost tourism by attracting an estimated 1 million sports fans.
The championship is set to become the biggest sports event to be held during Yanukovich's current term in office and is a matter of both prestige and business for the ex-Soviet nation.
But it now faces more potential boycotts by European politicians. EU Justice Commissioner Viviane Reding urged Michel Platini , president of European football's governing body UEFA, to raise the issue of Tymoshenko with Ukraine.
But German Olympic Sport confederation chief Thomas Bach sided with Voloshin, urging officials to avoid sports event boycotts which he said were not productive in politics.
Relations between Ukraine and the EU soured further this month by Tymoshenko's allegations that she had been beaten up by prison guards - an accusation denied by Ukrainian authorities.
Tymoshenko helped lead the 2004 Orange Revolution which doomed Yanukovich's first bid for the presidency, and has since served twice as prime minister but lost the 2010 presidential vote to Yanukovich in a close run-off.
The European Union has warned Kiev its members will not ratify milestone deals on political association and free trade with it as long as Tymoshenko remains in prison.
Yanukovich, who Tymoshenko says has personally orchestrated her conviction, has refused to intervene and prosecutors have heaped more charges on Tymoshenko leading to a new tax evasion trial which opened this month.
On the security front, a series of blasts in the city of Dnipropetrovsk last week which injured 30 people, have also added to concerns about the tournament.
The government said they had been organised by forces seeking to destabilise the nation. Hryhory Surkis, head of Ukraine's football union, has said the bombings targeted the championship itself.
Opposition leaders, on the other hand, have accused the government of trying to use the attack to divert public attention, both at home and abroad, from Tymoshenko's fate.