There have been several incidents in the recent past between the Assad regime and Turkey.
The Turkish troops are not fighting Syrian government forces and the attack would be the first assault on Turkish soldiers by the Syrian government forces.
Yıldırım also vowed "retaliation" against Syrian attack on Turkish troops, Hurriyet Daily News states. The attack came on the first anniversary of Turkey shooting down a Russian warplane over Syria, which prompted a lengthy diplomatic rift between Moscow and Ankara which ended in August.
The attack, carried out by "members of the Daesh (IS) terror group", took place in the Al Bab region of northern Syria where Turkish forces are supporting an offensive by pro-Ankara rebels, the privately-run news agency said.
"After that (Al Bab), we will go towards Manbij" to remove elements from the Syrian Kurdish Democratic Union Party (PYD) and People's Protection Forces (YPG) militia, Erdogan said.
"In the air strike assessed to have been by Syrian regime forces, three of our heroic soldiers were killed and 10 soldiers wounded, one seriously", the armed forces said in an online statement.
President Recep Tayyip Erdoğan and Prime Minister Binali Yıldırım were briefed on the attack by Chief of General Staff Gen. Hulusi Akar and Defense Minister Fikri Işık.
Turkey launched its military offensive inside Syria on August 24, seeking to oust Islamic State from a 60-mile stretch of the border days after blaming the group for a deadly bombing in the border city of Gaziantep.
The army statement said the wounded troops were evacuated from the area. Syrian Kurdish forces had liberated the town from Islamic State with USA support, despite warnings from Turkey that Ankara wouldn't tolerate their westward expansion. The 10 wounded soldiers were being treated at hospitals in Gaziantep and in the neighboring city of Kilis.
Since the offensive began, the rebels captured the IS stronghold of Jarabulus, cleared IS from Al Rai and retook the symbolically important town of Dabiq without much resistance.
The U.S. isn't aiding the push to take al-Bab because it is drawing Turkey and its rebel allies into a direct confrontation with the Kurdish forces that also want to seize the strategic town.
At least three Turkish soldiers have been killed in an air strike in northern Syria.
At the moment, the Turkish troops are not engaged in combat with Syrian government forces.