The explosion occurred around 1am near Taşkent, with the impact setting hills ablaze and heard for miles around.
President Mustafa Akıncı linked the incident to military operations in the Middle East but further investigations were under way by the military to establish what it was, he said.
"It is evident it is not something stemming from our soil . . . It is one of the bad sides of the war in the region falling into our country," he said.
Deputy Prime Minister and Foreign Minister Kudret Özersay said on social media initial assessments were that it was “a Russian-made missile . . . which was part of the air defence system that took place last night in the face of an air strike against Syria, completed its range and fell into our country after it missed".
Israeli warplanes fired missiles targeting Syrian military positions in Homs and the Damascus outskirts overnight in an attack that killed at least four civilians and wounded another 21.
If verified, it would be the first time that Cyprus has been affected by military operations in the Middle East despite its proximity to the region.
Officials were studying debris at the crash site, said Dr Özersay, adding: “The writings and signs on the debris will allow us to understand exactly what happened soon.”
A Greek Cypriot military analyst quoted by the Reuters news agency said pictures of the debris suggested it was a Russian-made S-200 missile.
Residents reported seeing a light in the sky then three loud explosions which were heard for miles around. Authorities evacuated some homes in the Taşkent area.
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