Turkey routinely carries out attacks in Iraq, where the PKK has bases and training camps in the Sinjar region and on the mountainous border with Turkey.
"Our heroic pilots successfully struck shelters, caves, tunnels, and ammunition depots belonging to the terrorist organization," Akar said.
"A large number of terrorists were neutralized," he said, adding that the scale of the operation will "further increase in the coming hours and days."
Akar would not say how many troops were involved in the operation, which he said started Sunday night.
Asked by AFP to comment on Turkey's operation, a PKK spokesperson in Iraq said on condition of anonymity: "The occupation army, which tried to land troops by helicopters, also wanted to advance by land.
"There are intense clashes between the Turkish army and HPG guerrillas," referring to the PKK's military wing.
The defense ministry said the operation was meant to thwart a large-scale attack against Turkey by the PKK.
Turkey has a long-running, cross-border campaign against the PKK and the Syria-based YPG forces. The latter, a predominantly Kurdish militia, was an integral force in the territorial defeat of the so-called Islamic State in Syria, liberating Raqqa, the Islamic State's de facto capital.