Poland and Ukraine are co-hosts of the month-long tournament whose opening games will be played on June 8. The final will be played in Kiev on July 1.
"At the very least, UEFA should transfer the final match of Euro 2012 from Kiev to Warsaw. Any other reaction will amount to silent acquiescence to the further undemocratic activities of the Ukrainian government," Jaroslaw Kaczynski, leader of the conservative Law and Justice party wrote in his blog.
"Flagrant human rights violations in Ukraine, as symbolised by the situation of jailed Yulia Tymoshenko, is the effect of disadvantageous political changes we are observing in Ukraine and proof of Ukraine's growing dependence on Russia."
Tymoshenko, main rival of President Viktor Yanukovich, was sentenced to seven years in prison last October for abuse of office after a trial that the West says was politically motivated.
She is now in a prison in the city of Kharkiv, one of the tournament venues. She has been on a hunger strike since April 20 in protest at what she said was an assault by prison guards, an allegation denied by the prison administration.
Several European politicians have said they intend to stay away from the former Soviet republic in protest.
Kaczynski seems to be a mostly lone voice in Poland with his call for a switch of venue. While Polish authorities have voiced their disapproval of how Tymoshenko's case is being handled, they have criticised calls for a boycott.
"The West should not boycott Ukraine during the European Championship in June as that would hamper its European ambitions and force the ex-Soviet country back into the arms of Russia," President Bronislaw Komorowski said this week.
Most Polish politicians have traditionally viewed a pro-Western Ukraine as an effective counterweight to Russian domination over Eastern Europe and have sought to draw it closer to the European Union.