Chancellor Angela Merkel is considering such a boycott, the German news website Der Spiegel reports.
Environment Minister Norbert Roettgen said the government should stay away from Ukraine during the tournament. Ukraine is co-hosting Euro 2012 with Poland.
Yulia Tymoshenko says she is very ill.
She is reported to be on hunger strike and on Friday images appeared showing bruises on her body, which she says prison guards inflicted. She is being held in Kharkiv, eastern Ukraine.
An official in the Ukraine Prosecutor’s Office, Vadim Goran, denied her allegation, saying the bruises came from “pushing against blunt, hard objects, or banging into them” and “in no way resulted from a punch to the stomach as she says”.
After seeing the photos Sweden’s Foreign Ministry summoned the Ukrainian ambassador and demanded an explanation.
Yulia Tymoshenko, key rival of Ukraine’s President Viktor Yanukovych, is serving a seven-year jail sentence for abuse of office and faces another trial on tax evasion charges.
The new trial has been delayed until late May because she is refusing to attend on health grounds. Yulia Tymoshenko accuses Viktor Yanukovych of exacting political revenge on her.
The authorities have denied her request to be treated abroad. She is said to have been suffering months of back pain and is reported to have been diagnosed with a herniated spinal disc.
Norbert Roettgen, quoted by Germany’s Bild newspaper, said the Ukrainian “dictatorship” must not be allowed to exploit Euro 2012 for its own benefit.
“That’s why I think visits by ministers and prime ministers to Euro 2012 are out of the question in current circumstances,” he said.
The German team will play the Netherlands in Kharkiv on 13 June. The tournament runs from 8 June to 1 July.
Germany’s Social Democrat opposition leader Sigmar Gabriel also called for a boycott.
On Thursday, Germany’s President Joachim Gauck called off his visit to a summit in the Ukrainian resort of Yalta next month. Czech President Vaclav Klaus has also cancelled his visit to Yalta for the central European leaders’ summit.
And on Friday the EU Justice Commissioner, Viviane Reding, said she would boycott Ukraine’s opening ceremony because “you cannot close your eyes on human rights, even during a great sporting celebration”.
Ukraine’s Foreign Ministry says it hopes the reports about Germany considering a boycott are just “a press canard”.
“We would not like to think that the political leaders of Germany are capable of reviving the methods of the Cold War and making sport a hostage of politics,” ministry spokesman Oleg Voloshin said.
In another blow to Ukraine’s image abroad the eastern city of Dnipropetrovsk – not one of the Euro 2012 venues – suffered four bomb blasts on Friday, which injured 27 people.
The authorities believe the attack – described as “terrorism” – was linked to a similar bomb blast in the city last November, in which the device was also placed in a rubbish bin.
Police have released photofit images of three suspects wanted in connection with Friday’s attack.
Fourteen victims remain in hospital in the city, two in a serious condition, Interfax-Ukraine news agency reports.
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