The incident came during a gun battle between Daesh terrorists and Iraqi Kurdish peshmerga forces on Saturday around the Gedu military base located in northern Iraq.
"Due to projectiles that fell on the base, our hero comrade has been martyred and one hero comrade was slightly injured," said the statement.
The army said the injured soldier was taking medical treatment at a state hospital in the southeastern Turkish province of Sirnak. Hours later, the General Staff said in another statement that the anti-Daesh international coalition led by the U.S. targeted Daesh positions in the northern part of Iraq.
"Four terrorist Daesh positions in the north of Iraq have been hit by warplanes of the [international] coalition," said the army.
"Right after, four additional targets were intensively shelled by Turkish Armed Forces planes; the targets were destroyed," the statement read.
Turkish Prime Minister Ahmet Davutoglu confirmed the Turkish warplanes targeted the Daesh position in Iraq in line with engagement rules in the aftermath of the incident.
"At the end of the assessment, we made with the General Staff chief, all positions that caused the martyrdom of our lieutenant were destroyed with the intervention of our air forces," Davutoglu told journalists at Ataturk Airport in Istanbul ahead of his departure for a two-day visit in Jordan.
Davutoglu said another air campaign was carried out with the participation of coalition warplanes, adding that Turkey had revealed its strong will and power in the wake of any attack that targeted its military presence abroad.
In his remarks, the prime minister defended Turkey's presence in Iraq, which he called "support for Iraqi brothers", and said this presence aimed at meeting the security needs of the Iraqi government.