Activists from Femen, known for its bold topless protests, said the 31-year-old Ukrainian had been found on Monday with a suicide note next to her body.
“It is with great regret and deep pain that I must confirm the death of Oksana,” said Inna Shevchenko, one of Femen's leaders, who also lives in the French capital.
Another Femen founder, Anna Gutsol, wrote on Facebook: “RIP. The most fearless and vulnerable Oksana Shachko has left us.
“We mourn together with her relatives and friends,” she said, adding that the group was awaiting “the official version from the police”.
Shachko was one of four feminist activists who founded Femen in Ukraine in 2008.
Exiled in France since 2013, she had since left the group and was working as an artist.
Operating under the slogan “I came, I stripped, I won,” Femen quickly drew attention around the world with its bare-breasted protests against sexism.
Their protests eventually started targeting authoritarianism and racism, with Russia's Vladimir Putin a particular target, alongside France's far-right
National Front party.
But in recent years the group has struggled with internal divisions as well as legal proceedings against its members.
In 2011, Femen said Shachko was among three members “kidnapped” by security agents and forced to strip naked in a forest after staging a topless protest mocking Belarussian strongman Alexander Lukashenko.
The agents had poured oil over the three women, threatened to set them on fire, and cut off their hair, Femen said.
She was abducted again by unknown assailants during a visit by Putin to Ukraine, according to the group.
Femen's lawyer said Shachko was beaten so badly that she was briefly hospitalised.