In a statement carried on the official news agency SANA, the military said several missiles were launched just after midnight from an area near Lake Tiberias that fell in the vicinity of the Mezzeh military airport on the western edge of the capital. It did not say whether there were any casualties.
The Syrian army statement said Israel through its attacks was assisting "terrorist groups" fighting the Syrian government.
“Planes of the Israeli enemy launched a number of rockets at 00:25 from the Kinneret area at the military airport of Mezzeh,” Syrian media quoted a military official.
Residents of Damascus reported hearing several explosions that shook the capital. The Mezzeh airport compound located on the southwestern edge of the capital had been used to launch attacks on rebel-held areas near Damascus and has come previously under rebel fire.
"The Syrian army command and armed forces warn the Israeli enemy of the repercussions of this blatant attack and stresses it will continue its war on terrorism," the army statement continued.
It was the third such Israeli strike into Syria recently, according to the Syrian government.
Israel has carried out sporadic attacks in Syria throughout the course of its civil war in an effort to prevent the transfer of weapons to the terror organization of Hezbollah.
According to the Lebanese newspaper Al Mayadeen which is affiliated with the terror group, four soldiers were wounded in the strike designed to eradicate ammunition and weapons stockpiles.
On December 7, the Syrian government reported Israel fired surface-to-surface missiles that also struck near Mezzeh airport. A week earlier, SANA said Israeli jets fired two missiles from Lebanese airspace toward the outskirts of Damascus, in the Sabboura area.
The Israeli military has declined to comment on those incidents, and there was no immediate comment on Friday's reported attack.
But Israel is widely believed to have carried out a number of airstrikes in Syria in the past few years that have targeted advanced weapons systems, including Russian-made anti-aircraft missiles and Iranian-made missiles, as well as positions of the Lebanese Hezbollah group in Syria.
The Shiite group has sent thousands of its fighters to Syria to support President Bashar Assad's forces in the country's civil war, now in its sixth year.
Israeli Defense Minister Avigdor Lieberman recently reiterated his government's position to not get involved in the Syrian war.
In December last year, a Syrian military official also said that Israel attacked the Mezzeh airport, causing a series of explosions
Roi Kais contributed to this report.