The defence ministry said it had been "engaged and neutralised by NATO air-and-missile defence assets deployed in the eastern Mediterranean".
It did not specify the missile's intended target. Iran has been hitting sites across the region in retaliation after the United States and Israel launched strikes against it on Saturday.
A Turkish official, speaking to AFP on condition of anonymity, said the missile had been "aimed at a base in Greek Cyprus but veered off course".
Officials said fragments that fell in the Dortyol district in southern Turkey, near the Syrian border, had been identified as pieces of the interceptor used to neutralise "the threat in the air".
No casualties were reported.
Reacting to the incident, US Secretary of State Marco Rubio said in a call with Turkey's Foreign Minister Hakan Fidan "that attacks on Turkey's sovereign territory were unacceptable and pledged full support from the United States," State Department spokesman Tommy Pigott said.
The incident also drew condemnation from NATO.
"NATO stands firmly with all allies, including Turkiye, as Iran continues its indiscriminate attacks across the region," NATO spokeswoman Allison Hart said, using Turkey's official name.
"Our deterrence and defence posture remains strong across all domains, including when it comes to air and missile defence."
The United Arab Emirates "strongly condemned" the missile launch as a "serious escalation", the foreign ministry said in a statement.
Ankara summoned the Iranian ambassador to convey its "reaction and concerns" over the incident while Fidan warned Tehran against steps that could widen the conflict, a diplomatic source said.
Fidan told his Iranian counterpart Abbas Araghchi in a phone call that "any steps that could lead to the spread of conflict should be avoided", the source added.
Iranian news agency Tasnim said Araghchi told Fidan that Iran's retaliatory strikes were aimed at bases used to carry out operations against the Islamic republic.
Turkey hosts a number of military facilities used by the United States and other NATO allies.
- 'Wrong strategy' -
In an evening address, President Recep Tayyip Erdogan said Turkey was "taking all the necessary precautions" in consultation with its NATO allies and was issuing "warnings in the clearest terms to prevent similar incidents from happening again".
"If we, as a nation, want to live in peace and tranquility... we must constantly increase our deterrent capabilities. In these difficult times... we are leaving absolutely nothing to chance regarding the security of our borders and airspace," he said.
Turkey, a majority Sunni Muslim NATO member, shares a 500-kilometre (315-mile) border with Iran.
Erdogan has described the US-Israeli strikes on Iran which sparked the conflict as "illegal" and Fidan also criticised Iran's retaliatory strikes against Gulf nations and beyond, saying it was the "wrong strategy".
"The underlying strategy seems to be: 'If I am going to sink, I will take the region down with me'," Fidan said in an interview late Tuesday.
Analysts said the trajectory of the Iranian missile and its destruction by NATO systems further raised the stakes for a widening regional war, even if there was no clear evidence Iran intended to strike Turkey.
"Turkey will not want to become embroiled in the US-Israel attack on Iran, which it has criticised, but if Iran launches more missiles clearly aimed at targets on Turkish territory, Ankara will consider its own direct retaliation," said Hamish Kinnear of risk-intelligence firm Verisk Maplecroft.
The defence ministry said: "Any steps necessary to defend our territory and airspace will be taken decisively and without hesitation."
"We reserve the right to respond to any hostile actions directed at our country," it added.
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