Zana came to prominence in 1994 when she was convicted for links to the PKK, which is outlawed in Turkey.
She was released in 2004 after Turkey's appeals court overturned her conviction and that of three other Kurdish former politicians.
Barroso visit
The latest conviction came as Jose Manuel Barroso, the European Commission president, arrived in the capital Ankara for talks on moves needed to advance Turkey's troubled EU membership bid.
Central to those reforms is a move to soften a law, article 301 of the penal code, which has been used against hundreds of writers including Orhan Pamuk, the Nobel literature laureate, for insulting "Turkishness".
A legal amendment to the article, likely to be passed next week, is weaker than Brussels might have hoped, with writers still liable to prosecution for insulting the Turkish nation.
However, the president would now have to give the green light for any such trial to proceed.
Fighters killed
Meanwhile, Turkish troops on Thursday killed 11 PKK fighters in clashes near the city of Tunceli in eastern Turkey, the provincial governor's office said.
Troops have been hunting Kurdish fighters around Tunceli since a roadside bomb attack targeted a military convoy in the area on Wednesday.
The bomb went off after the convoy passed and no one was harmed.
The conflict between the PKK and the government has claimed the lives of tens of thousands of people since the fighters took up arms in 1984.
Turkey's military launched a ground assault against PKK camps inside Iraq in February and there have been sporadic clashes along the border and inside Turkey since then.