One Turkish soldier died on Friday in clashes with "terrorists" from the outlawed Kurdistan Workers' Party (PKK) in the operation area in northern Iraq, the defence ministry said in a statement.
Turkey launched an air and ground offensive against Kurdish rebels in northern Iraq on Wednesday, calling it Operation Claw-Tiger.
The defence ministry said the Turkish soldier was wounded "in clashes with terrorists in the Operation Claw-Tiger area" and died in hospital later, without providing details where exactly the clashes were.
The militants' targets across the border came under "intense" Turkish fire, it added.
The Turkish military regularly carries out operations against PKK hideouts in southeast Turkey and its rear bases across the border.
The PKK, which has fought an insurgency against the Turkish state since 1984, is banned as a terrorist group by Ankara and its Western allies.
Turkey's latest operation has drawn protests from Baghdad which demanded Ankara immediately halt its assault in northern Iraq.