Attempts to agree a bill that would allow Tymoshenko to leave the country for medical treatment have stalled.
The EU has made the move a condition before it signs an association and free trade deal with Ukraine this month.
But Ukraine has come under intense pressure from Russia not to sign.
Russia wants Ukraine to join its own customs union with Kazakhstan and Belarus, which it sees as a prototype rival to the European Union.
Ukraine`s President, Viktor Yanukovych, made a secretive visit to Moscow at the weekend.
`Stab in the heart`
MPs said on Wednesday that attempts between the government and opposition to finalise a bill allowing convicts to receive medical treatment abroad had failed.
The bill was meant to allow Tymoshenko to be handed over for medical treatment in Germany.
The former prime minister, and long time bitter rival of President Yanukovych, has been serving a seven-year jail term since being convicted of abuse of power in 2011 over a controversial gas deal with Russia.
The parliamentary leader of Tymoshenko`s opposition Fatherland group, MP Arseniy Yatsenyuk, blamed the president`s ruling Party of the Regions for the failure of the bill, and said it was deliberately trying to destroy the EU deal.
"They are hindering Ukraine`s movement towards the European Union," he said.
EU monitors are in Ukraine and were hoping to witness the vote go ahead on Wednesday, before making their recommendation on whether the bloc should sign an agreement with the country at a summit in Vilnius at the end of the month.
The EU has been attempting to build closer relations with neighbours that were once part of the Soviet Union, and is expected to initial but not yet formally sign association agreements with Georgia and Moldova.
Tymoshenko on Tuesday accused President Yanukovych of seeking to undermine the country`s EU aspirations.
"Yanukovych wants to convince European leaders that their efforts to protect Ukraine against dictatorship are futile, and they have to give up and retreat," she said in a statement read by her daughter.
And she said the arrest of her own lawyer, Serhiy Vlasenko, on suspicion of domestic violence on Tuesday, was "the last stab" in the heart of closer relations with the EU.
The EU has made clear it believes the judicial campaign against Tymoshenko has been politically motivated.
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