Nusaybin, a district of Turkey's southeastern province of Mardin on the Syrian border, has been under curfew since Sunday. Eight policemen were also injured in the clashes, Reuters reported.
Eastern Turkey has suffered months of violence since a ceasefire with the Kurdish militant group PKK ended in July and the fighting shows little sign of tailing off.
Last month, Kurdish militants scrapped a separate unilateral truce - called in the wake of an ISIL suicide bomb attack in Ankara - after President Tayyip Erdogan and his AK Party, which won back its parliamentary majority in a November election, vowed to wipe out the PKK.
More than 40,000 people have been killed in the insurgency since it began in 1984, as the Kurds, roughly a quarter of the Turkish population, fight for cultural and political rights and self-determination.
The PKK is designated as a terrorist group by Turkey, the United States and the European Union but not by the United Nations.