Tymoshenko is serving a seven-year prison sentence in Ukraine after being convicted on charges she abused her authority when she helped broker a 2009 natural gas deal with Russian energy company Gazprom. She denies the charges and claims prison authorities have abused her.
Pia Ahrenkilde Hansen, a spokeswoman for the European Commission, said leaders in Brussels won't attend any events in Ukraine given growing concerns about Tymoshenko's treatment.
Dennis Abbot, a spokesman for the European Sports Commissioner Androulla Vassiliou, said there was growing frustration with Kiev given plans for the Euro 2012 soccer tournament in May.
"If the current situation stands -- this situation regarding human rights in Ukraine, and in particular the situation regarding the treatment of Mrs. Tymoshenko and other opposition figures -- then the commissioner feels that it would be entirely wrong to go to Ukraine," Abbot was quoted by Radio Free Europe/Radio Liberty as saying.
Kiev charged European officials were "making sports a hostage of politics" by adopting "Cold War" policies.
At least two dozen people were injured in a series of bomb explosions Friday in the Ukrainian city of Dnepropetrovsk, Tymoshenko's home town.