The Turkish General Staff said 11 soldiers were also injured when the jet mistakenly hit a building where Turkish units were located.
The military said the incident occurred at around 8.40 a.m. local time (0540 GMT) in the region where Operation Euphrates Shield remains active.
The wounded soldiers were immediately transported to a hospital.
In a phone call to President Recep Tayyip Erdogan, his Russian counterpart Vladimir Putin expressed condolences over the "tragic" incident, the Kremlin said in a statement Thursday.
The leaders exchanged views on key aspects of the Syrian crisis within the framework of the joint fight against international terrorism, it said.
The statement added the leaders agreed to step up military coordination during operations in Syria against Daesh and other extremist groups.
"Both leaders affirmed their readiness to continue active efforts to advance the Astana [Kazakhstan peace talks] and Geneva processes on resolving the Syrian conflict," it said.
In a phone call, Russian Chief of General Staff Gen. Valery Gerasimov also conveyed condolences to his Turkish counterpart Hulusi Akar, the Russian Defense Ministry said in a statement.
Later Thursday, Turkey's Economy Minister Nihat Zeybekci expressed condolences to families of the martyred soldiers during a meeting at the Turkish parliament and said "these kind of mistakes in war regions are possible though it's of minimal chance."
Turkey's main opposition Republican People's Party (CHP) leader Kemal Kilidaroglu also wished God's mercy upon the martyred soldiers on his official Twitter account.
Operation Euphrates Shield, which involves Free Syrian Army fighters backed by Turkish forces, was launched last August to secure Turkey’s border with Syria against terrorists and support opposition forces.
Since November last year, the operation has focused on taking the town of Al-Bab, 30 kilometers (19 miles) south of the Turkish border, from Daesh.
Syria has been locked in a devastating civil war since early 2011, when the Bashar al-Assad regime cracked down on pro-democracy protests – which erupted as part of the Arab Spring uprisings – with unexpected ferocity.