The woman, identified as Ebru Firat, was detained following a tip-off after she flew into the city's Ataturk airport, the agency said.
It said the woman, whose code name was "Amara", could have come to the city to stage an attack. The agency said the woman had in the past been photographed next to Murat Karayilan, one of the PKK's top leaders in northern Iraq.
Fresh tragedy: Child bomber kills 51 wedding guests in Turkey
The pro-government Sabah daily said Firat had been detained after arriving on a flight from Diyarbakir in the Kurdish-dominated southeast and had been planning a suicide bombing in Istanbul.
The PKK has killed hundreds of members of the Turkish security forces mainly in the southeast of the country since a ceasefire disintegrated last year.
And a splinter group of the PKK, the Kurdistan Freedom Falcons (TAK), has claimed two car bomb attacks in Ankara and one in Istanbul this year that left dozens dead.
13 killed in Turkey ‘bomb attacks, cross-border fire’
Over 40,000 people have been killed since the PKK first took up arms in 1984 with the aim of carving out an independent state for Turkey's Kurdish minority.
It is proscribed as a terrorist group by Turkey, the European Union and the United States.
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