Security forces are searching for the prisoners, who escaped overnight, Today's Zaman said.
They have been convicted of or charged with belonging to the PKK and abetting the militants,
Four of the men were on trial and 14 had been convicted, court officials said.
Authorities said they suspect the prisoners are hiding in a mountainous area in Bingol province.
The escape comes as Prime Minister Tayyip Recep Erdogan prepares a package of reforms to end the conflict with the PKK, Today's Zaman said.
The PKK has been fighting for autonomy for the southeastern region for three decades, and the conflict has killed more than 40,000 people.