Another two soldiers were wounded during fighting, said the ministry statement, which did not say where this took place. An earlier toll provided by the military had three soldiers killed and four wounded.
Turkey's official news agency Anadolu said the Turkish soldiers had clashed with fighters from the Kurdistan Workers' Party (PKK), which Ankara and its western allies say is a terrorist organisation.
The PKK has training camps and bases in autonomous Iraqi Kurdistan and has been waging an insurgency against the Turkish state since 1984, a conflict that has killed 40,000 people, many of them civilians.
Ankara has launched a series of operations against PKK fighters in Iraq and Syria, the latest one in northern Iraq beginning in April.
Turkish President Recep Tayyip Erdogan said on Monday that Turkey would soon launch a new military operation into northern Syria which he said was designed to create a 19-mile (30-kilometre) "security zone" along their border.
Since 2016, Turkey has also launched three offensives into northern Syria against the People's Protection Units (YPG), a Syrian-Kurdish group it considers to be part of the PKK.
Turkey wants to use these security zones to keep Kurdish militants at a safe distance – and to house some of the 3.7 million Syrian refugees currently sheltering inside its own borders.