Turkish Prime Minister Binali Yildirim announced the deaths in a televised address on Saturday.
Earlier, Turkish President Recep Tayyip Erdogan had said an army helicopter had been “shot down” near the southern Hatay province.
“These things will happen, we are in a war … We might lose a helicopter, but they’ll pay the price for this,” he said in Istanbul.
The state-run Anadolu agency, citing the Turkish army, said the ATAK aircraft crashed at around 1pm local time (10:000 GMT).
Mustafa Bali, a spokesman for the Kurdish YPG armed group, told the AP news agency that his fighters downed the helicopter in Raju, northwest of the Syrian city of Afrin.
Turkey opened a new front in the multi-sided Syrian civil war, when it launched an air and ground offensive against YPG fighters on its southern border with Syria last month.
The YPG - trained, armed and supported by the US to fight against the Islamic State of Iraq and the Levant (ISIL) - control a swathe of land in northern Syria.
Turkey considers the YPG as an extension of the outlawed Kurdistan Workers Party (PKK), which has fought a bloody, decades-long armed campaign.
SOURCE: AL JAZEERA AND NEWS AGENCIES