The Turkish military statement said the soldiers who were killed were deployed in northern Syria when they were targeted at about 03:30 (00:30 GMT) in an air strike that it "assessed to have been carried out by Syrian regime forces".
Earlier, Turkish media reported that the attack in the Al-Bab region was carried out by Islamic State (IS) militants.
The group's director, Rami Abdurrahman, said the suicide attack occurred in the rural area of al-Bab, near a village called Waqqah and dismissed reports of an airstrike. One of the wounded soldiers was said to be in critical condition.
If the attack is confirmed to be a Syrian government airstrike, it is likely to ratchet up tensions between Ankara and Damascus.
Turkey is part of the US -led coalition against Islamic State, but Washington has said it is not providing support for the three-month-old Turkish offensive in Syria as it moves toward the Islamic State-held city of al-Bab.
The Turkish troops are not fighting Syrian government forces, and have not been attacked by them, though Damascus has strongly objected to the military intervention. "There will certainly be retaliation against these attacks".
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The Turkish military launched an operation - dubbed "Euphrates Shield" - with tanks and air power in August to support Syrian opposition fighters seeking to retake territory from IS in northern Syria.
It comes exactly a year after Turkey became the first North Atlantic Treaty Organisation member since 1952 to down a Russian jet, saying the plane violating its airspace from Syria, a move that triggered a war of words and prompted sanctions by Moscow. The dead and injured were taken to hospitals in Turkey's southern Kilis and Gaziantep provinces.
Turkish authorities have banned distribution of images relating to the Syria attack within Turkey.
The operation aims to push IS militants, 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 militants. Thursday's strike, said the USA official, "further complicates an already complicated situation". Turkey has been calling for Mr. Assad's ouster and pushing for a safe zone in northern Syria since late 2011.
"We reached Al Bab right now and besieged it from the west", the president said in a speech on Tuesday.
Dion Nissenbaum in Istanbul, Noam Raydan in Beirut, Yaroslav Trofimov in Ankara and Julian E. Barnes in Brussels contributed to this article.