The PKK has waged an insurgency inside Turkey since 1984 that has left tens of thousands dead.
Sara Aktas was detained at Ataturk International Airport while seeking to travel to Germany, the state-run Anadolu news agency said.
It said she is accused of being a key figure in the Kurdistan Communities Union (KCK), which the authorities regard as the urban wing of the outlawed Kurdistan Workers Party (PKK). She faces up to 15 years in jail on charges of membership of an armed "terror" group, it said.
Turkish authorities have stepped up arrests of activists, journalists and even politicians suspected of links to the PKK in the wake of the July 15 failed coup.
Critics say that the state of emergency implemented in the wake of the coup has gone well beyond seeking to punish the coup plotters themselves.
MPs from the pro-Kurdish Peoples' Democratic Party (HDP) strongly disputed the official version of events, saying that rather than being a member of the KCK, Aktas is part of the Kurdish Free Women's Congress (KJA).
HDP MP Dilan Dirayet Tasdemir said on Twitter that rather than trying to escape Turkey, Aktas had been returning from Igdir in the east of the country with her nephew.
Another HDP MP, Besime Konca, rubbished reports that Aktas had been travelling on a fake passport under a false name, saying she had been simply returning to Istanbul from Igdir.
The PKK has waged an insurgency inside Turkey since 1984 that has left tens of thousands dead. Violence renewed in July 2015 after the collapse of a two-and-a-half year ceasefire.
Ten MPs from the HDP, including the two co-leaders, were arrested earlier this month on charges of links to the PKK which they deny.