The attack took place at 11:15pm (21:15 GMT), it said.
Israeli warplanes fired several missiles towards Damascus late Friday, Syrian state media reported.
The London-based Syrian Observatory for Human Rights war monitor said that the strikes targeted "two areas hosting military positions of Iranian forces and the Lebanese Hezbollah movement".
Al Arabiya quoted the Syrian state news agency SANA as stating that one of the airport warehouses was hit during the attack.
"Only a ministry of transport warehouse at Damascus worldwide airport was hit", SANA cited the military source as saying.
Following the airstrike, Israeli warplanes were seen flying at high speed and low altitude over the southern Lebanese city of Tyre.More news: Leishman fifth as Kuchar leads PGA Hawaii
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This was the first Israeli attack on Syria since Christmas Day, when an errant Syrian anti-aircraft missile landed in Israeli occupied territory, sparking a flurry of Israeli attacks.
It is not yet clear whether the S-300s were among the air defense systems used in the Friday night counterattacks.
Israel has not responded to the allegations it was involved in that incident, but previous Israeli air strikes inside Syrian territory have drawn criticism and recently caused tensions with Russian Federation, an ally of Syrian President Bashar al-Assad.
Israel also insists that Iran uses Syria as a bridge to supply missiles and other weapons to Hezbollah in Lebanon.