Vlasenko could lose his seat in parliament following a complaint from a member of President Viktor Yanukovych's Party of the Regions.
Vlasenko has violated the law by failing to give up his lawyer's licence as deputies are supposed to do, the complaint says. Vlasenko says he had filed the necessary papers in time.
Tymoshenko, a fierce critic of the president, was sentenced to seven years in prison in October 2011 on charges of abuse of office. She has been treated for back problems in a state hospital since last May.
Her case has soured Ukraine's ties with the West, which saw it as an example of selective justice. The European Union has delayed the signing of deals on trade and political association with Kyev over the issue.
In a statement released by her Batkivshchyna (Fatherland) party, Tymoshenko accused Yanukovych and his allies of seeking revenge through attacking one of her allies in parliament.
"He is guilty of only one thing - defending me," Tymoshenko said.
Catherine Ashton, the EU foreign policy chief, and Štefan Füle, the enlaregment commissioner, said they were "deeply concerned" about the treatment of Vlasenko in a statement.
Ashton and Füle called on the Ukrainian authorities “to address this situation so as to avoid creating any perception of misuse of the judiciary for political purposes.”
They also said the Law on the Election of People's Deputies establishes a five-day time framework for the results of the elections to be challenged before the courts. “Legal proceedings which come months after the confirmation of the final election results raise political and legal concerns,” Ashton and Füle said in the statement.
Court postpones trial
Also on Tuesday, a Ukrainian court again postponed the start of the trial of Tymoshenko on tax evasion and embezzlement charges after she refused to attend the hearing on health grounds.
The new tax evasion trial, based on charges that date back to the 1990s when Tymoshenko ran a large gas trading business, has dragged on since April 2012 with hearings being routinely delayed due to her absence.
A district court in the city of Kharkiv adjourned the hearings until 22 March, the Interfax news agency said.
Tymoshenko's initial conviction was related to a 2009 gas supply deal with Russia which she brokered as prime minister. Yanukovych's government says the deal saddled Ukraine with an exorbitant price for gas for the next 10 years.
In what could become the third and the most serious case against her, Tymoshenko has been accused by state prosecutors of being behind a 1996 contract killing of a local businessman and parliament deputy.
Tymoshenko, one of the leaders of the 2004 Orange revolution protests that derailed Yanukovych's first bid for the presidency, has dismissed all charges against her as a vendetta by the president.