Ankara shut down air links on Monday and the freeze on flights would last until at least July 3 before being reviewed, said the ministry statement.
"This decision has been taken in the context of the intensification of activities of the PKK at Sulaimaniyah, the intrusion of the terrorist organisation at the airport and the threat it poses to air security," it said.
The governor of Sulaimaniyah province, Haval Abu Bakr, urged Ankara to "revise" its decision.
"I can tell you that Sulaimaniyah and its airport are secure," he told AFP, adding that "initiatives" were under way between those concerned.
Airport spokesperson Dana Mohammed said that under normal circumstances, one daily civilian flight linked Sulaimaniyah to Turkey.
The Kurdish-led Syrian Democratic Forces (SDF) said last month that one of its top commanders was among nine fighters killed when two helicopters crashed in Iraq in mid-March.
They had been heading to Sulaimaniyah in Iraq's autonomous Kurdistan region for talks on security and military issues.
The SDF has been a key ally of the US-led coalition fighting jihadists of the Islamic State group in Syria and neighbouring Iraq.
Turkey and its Western allies consider the PKK to be a "terrorist" organisation.
But Turkey also considers the dominant faction in the SDF, the People's Protection Units (YPG), as an offshoot of the PKK.
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