Wearing only mini-shorts and high heels, she performed her stunt inside Istanbul's Sabiha Gokcen airport, on the Asian side of the bi-continental city.
The woman, with the words "Air Dictator" painted in red on her chest, brandished a banner representing a plane ticket that read "Erdogan, from: Istanbul to: Kabul".
Police arrested her after the brief protest.
Femen said in a statement it "urges the people of Turkey, like Egyptians, to overthrow Erdogan's Islamist regime and force Erdogan to relocate to a country close to him in spirit (such as) Iran, Afghanistan and Pakistan."
The nationwide protests left four people dead and scores wounded.
The perceived islamisation of Turkish society during Erdogan's 10-year-old rule was one of the demonstrators' main grievances.