According to the Israel Defense Forces, the remnants of the missile were found in an open field on the Golan heights.
The Israeli military denied any of its assets were hit but stopped short of denying it had conducted strikes at all.
Abdel Rahman said Thursday was the first time the Assad regime's air defenses had been called into action since the incident on September 17 in which 15 Russians were killed.
Syria said Israeli warplanes attacked a military outpost in Kisweh in May.
The state news agency said the attack was foiled and did not admit to any losses.
The attack against Syrian sites in the town of Kisweh south of Damascus was carried out by Israel, the ministry said, Xinhua news agency reported.
On Friday, a senior Syrian defense official refuted previous reports of air defense hitting an Israeli plane.
The Syrian Observatory for Human Rights watchdog reported that two missiles on Thursday night hit a warehouse near the Jabl al-Mana area south of the capital.
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"Reports regarding an [Israeli army] aircraft or an airborne [army] target having been hit are false", it said in an English-language statement.
"Air defense intercepts hostile targets over al-Kiswah and downed them", a military source was quoted as saying by Syria's SANA news outlet.
Kisweh, where Thursday's strikes were reported, is situated some 35 kilometers west of Israel's northern border and has been targeted by Israel in the past. Troops are scanning the area. Using this pretext, Tel Aviv has struck alleged positions of Iranian and Iran-backed forces across Syria over the course of the seven-year conflict.
Working to prevent the entrenchment of Iranian forces and the transfer of advanced weaponry to Hezbollah, the Israel Air Force has admitted to carrying out hundreds of airstrike in Syria.
Moscow pinned responsibility for the downing of its jet on Israel, saying its plane used the larger Russian one for cover, an allegation Israel disputed.
Russian Federation subsequently upgraded Syrian air defences with the delivery of the advanced S-300 system, which Damascus said last month would make Israel "think carefully" before carrying out further air raids in Syria.
Since then Israel has been very careful with its operation over Syria. There is no indication that finding anything, or those missiles doing anything, would have any impact on continued Israeli strikes.