The attack occurred at around 3:30 am (0030 GMT) in the course of a Turkish-led Syrian rebel operation in northern Syria, the army statement said. It said the wounded soldiers were evacuated rapidly from the area, Reuters reported.
It would be the first time Turkish soldiers are known to have been killed by Syrian government forces in the offensive, dubbed Euphrates Shield, which was launched on Aug. 24.
The operation reportedly aims to push Daesh (ISIL or ISIS) terrorists, as well as the Kurdish YPG militia, away from the Syrian side of Turkey's border and has advanced to near the city of al-Bab, which is controlled by the extremists.
Earlier, security and hospital sources in Turkey said Daesh militants had carried out an attack which killed three Turkish soldiers in the al-Bab region.
They said the wounded soldiers were transferred to hospitals in the Turkish border provinces of Kilis and Gaziantep.