The woman was gunned down in a shootout with police in the city of Istanbul, according to the official Anatolia news agency.
She was allegedly a member of the Marxist Revolutionary People's Liberation Party-Front (DHKP-C).
Operations have taken place in 13 cities, with 251 suspects detained so far, according to Anatolia.
The operation in Istanbul involved some 5,000 Turkish police forces who went into action on Friday to apprehend suspected members of the ISIL terror group and the Kurdistan Workers Party (PKK).
The operation also targeted suspected members of the PKK's youth wing, the Patriotic Revolutionary Youth Movement (YDG-H), and the DHKP-C, Anatolia added.
It is not yet clear how many people were arrested in the Istanbul operation, which also involved helicopters.