Femen said Inna Shevchenko had been under 24-hour surveillance by officers of the Security Service of Ukraine for two weeks and the group feared she might be arrested.
"The organization's council ruled to evacuate activist Shevchenko to Paris, where she could continue her work," Femen said on its website.
Shevchenko left her apartment via the balcony, then drove a car to Korosten, where she boarded a train to Warsaw.
In an interview with the 1Ư TV channel, Femen said it planned to open a "Femen training center for activists" in Paris, where "activists from Europe and all over the world will be invited".
A video posted online Aug 17 showed a topless blond Femen protester wearing red shorts, with the words "Free Riot" scrawled across her chest and arms, cutting the cross with a chainsaw and then pulling it down using a rope pulled by two other activists, and then posing with her arms extended crucifix-style.
The cross was put up on a high hill near Kiev's Independence Square during the 2004 pro-democracy Orange Revolution.
The activists warned Russian President Vladimir Putin and Patriarch Kirill that they would "turn the blade of our chainsaw" against those "responsible for the suffering of innocent women" if the Pussy Riot members are jailed.