Kabaeva, 38, is a former Olympic gymnast and gold medalist who is widely believed to be Putin's "mistress" and mother to "secret" children whom he has never officially recognised, Daily Mail reported.
The petition comes amid reports that Kabaeva, once named "Russia's most flexible woman", was sent to a private chalet in Switzerland earlier this month amid the invasion of Ukraine.
"It's time you reunite Eva Braun with her Fuhrer," said the strongly-worded petition which was posted on change.org in in German, French and English and has so far received over 57,000 signatures.
"Despite the current war, Switzerland continues to host an accomplice of Putin's regime," the petition has claimed.
The pair have been pictured together on several occasions, and investigations by the Anti-Corruption Foundation, set up by jailed Putin opponent Alexei Navalny, "revealed several Russian oligarchs have inexplicably bestowed gifts of property, money and other assets upon Kabaeva's family".
The former gymnast is seldom seen in public, but she was caught on video dancing at the "Divine Grace" rhythmic gymnastics tournament in Moscow in December last year, mere weeks before Russia invaded Ukraine.