"Our air defences intercepted hostile targets over the skies of Damascus," state agency SANA said.
It said the "missiles were launched from over the occupied Golan Heights".
Several missiles were intercepted before they could reach their targets, it added.
A Syrian army source quoted by SANA said the attack took place at 11:45 pm (21:45 GMT), when an AFP correspondent in Damascus heard loud blasts.
SANA released a video of what appeared to be Syrian air defences firing over Damascus.
The Syrian Observatory for Human Rights blamed the attack on Israel, which has not claimed responsibility.
Israel does not usually comment on such attacks.
The Britain-based monitor said the attack targeted Iran-backed militias near the capital. It said some missiles hit their intended targets, which included a weapons depot near the airport.
Israel has repeatedly bombed Iranian-backed militia targets in Syria, saying its goal was to end Tehran's military presence in the country.
Earlier this month, Israeli air strikes killed 23 Syrian and foreign fighters in Syria.
Three Iranians and seven Tehran-backed foreign fighters were among those killed in the February 6 raids, according to the Observatory.
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