Five other soldiers were injured when two improvised explosive devices exploded on Monday in the Zap region of northern Iraq, not far from Turkey’s southeastern border.
The army blamed a “separatist terrorist organization” — Turkey’s official term for the outlawed Kurdistan Workers’ Party (PKK) — for the blasts.
Clashes broke out immediately after the first of the attacks, the military said, as it reported it had killed 16 PKK members in air strikes in the past 24 hours.
It was not possible to independently verify the toll.
Since the PKK launched its insurgency in Turkey in 1984, over 40,000 people have been killed. The group is blacklisted as a terrorist organization by Ankara, the United States and the European Union.
After the collapse of a two-year cease-fire in 2015, Turkish military operations against the PKK intensified in southeastern Turkey.
Turkey regularly conducts air raids against PKK militants who have rear bases in the Qandil mountain area of Iraq, while Turkish ground troops sometimes stage incursions into the area.
The incident comes at a time of high tensions in Iraq following the controversial non-binding independence vote held by Iraqi Kurdistan last month, which was bitterly opposed by Turkey and Baghdad.
The blasts took place outside areas held by the Iraqi Kurdistan Regional Government.