The EU has voiced concern over the fate of opposition leader Tymoshenko, but has failed to decide on a joint boycott of the Euro 2012 tournament, which is being co-hosted by Poland and Ukraine.
The Dutch have said they will not send any political representatives, and nor will the European Commission. Other countries, such as Germany, have said their attendance is linked to Tymoshenko's fate.
The former prime minister says she has been beaten and her health has deteriorated rapidly since her imprisonment last October, which the EU has said is politically motivated.
"No member of the government will travel to Ukraine during the European championships", France's newly-appointed Sports Minister Valerie Fourneyron said on the sidelines of a friendly match between France and Serbia.
"The decision has been taken as a result of Mrs. Tymoshenko's situation," she said, adding she had informed Ukrainian authorities and that France's national team would still play in the tournament.
Tymoshenko, the main opponent of President Viktor Yanukovich, was sentenced to seven years in prison on charges of abusing her power as prime minister in forcing through a 2009 gas deal with Russia.
She has denied any wrongdoing and says Yanukovich is pursuing a vendetta against her.
But Ukraine authorities have kept up the pressure, adding accusations of tax evasion, and on Wednesday said they were looking into her possible involvement in a 16-year-old contract killing.
In an interview with BBC News on Thursday, Yanukovich said he was aware that Tymoshenko's case could hinder Ukraine's integration into the EU.
But he said the legal process was still ongoing.
"We have approached foreign lawyers... they will carry out a legal audit of Tymoshenko's case. Very soon we will hear their findings," he said, but did not elaborate.
Tymoshenko remains in prison in the city of Kharkiv, one of the Euro 2012 venues, and is on hunger strike in protest at what she said was an assault by prison guards, an allegation denied by the prison administration.