The chief of the European Union's head office says he will not go to Ukraine unless there is a swift improvement in the human rights situation there.
EU Commission President Jose Manuel Barroso's announcement followed that of EU Justice Commissioner Viviane Reding, who is skipping the ceremonial Euro 2012 opening on June 8.
Ukraine is co-hosting the tournament with Poland. But the jailing of Tymoshenko, concerns over lack of infrastructure and accommodation, and a series of mysterious bomb blasts in the city of Dnipropetrovsk last week, have all combined to create a less-than-ideal backdrop for the tournament.
Tymoshenko is being held in a prison in Kharkiv, one of the venues for the Euro 2012 tournament.
Germany will play a match against the Netherlands in the city.
All three of the England team's group games will be in Ukraine.
Czech President Vaclav Klaus cancelled his visit to a summit of Central European leaders being held on May 11-12 in Ukraine because of Tymoshenko's treatment, his spokesman said. German President Joachim Gauck said he also will not travel to the Yalta gathering.
Photographs surfaced last week of bruises on Tymoshenko's body, which she says were inflicted by prison guards.
The Ukrainian Government has insisted that Tymoshenko's jail term, for overstepping the powers of office when she was Prime Minister, is a court matter and not one in which the President can intervene.
- Independent, AP