The AS532 Cougar helicopter crashed shortly after taking off from a base in Sirnak province bordering Iraq, killing all 13 onboard, it said in a statement.
"Our hero comrades in the helicopter fell as martyrs," the army said.
Initial findings showed the crash was the result of an accident, the military statement said, adding that an investigation was underway.
Turkey's chief of staff, General Hulusi Akar, travelled to the region to carry out an inspection, Anadolu said.
Deputy Prime Minister Mehmet Simsek, Defence Minister Fikri Isik and Interior Minister Suleyman Soylu were also travelling to the region, it added.
President Recep Tayyip Erdogan was briefed about the accident after chairing the country's top National Security Council meeting in Ankara, the state-run Anadolu news agency reported.
In a separate statement, the local governor's office said rescue teams had been dispatched to the scene.
In March, seven people, including four Russians, were killed when a privately-owned helicopter crashed in Istanbul after hitting a television tower.