The Sana news agency said air defences intercepted most of the missiles, but that eight people were wounded.
A monitoring group said Syrian army positions and those of Iran-backed militias were hit, killing 12 fighters.
Israel did not comment, but it has acknowledged carrying out hundreds of strikes in Syria in recent years to stop Iranian “military entrenchment”.
Iran and its proxies, including the Lebanon’s Hezbollah movement, are supporting forces loyal to President Bashar al-Assad in the country’s civil war.
Sana cited a Syrian military source as saying that Israeli warplanes flying over Lebanon and the occupied Golan Heights launched two waves of missiles at southern Syria early on Thursday.
The first wave targeted military positions in the suburbs of Damascus, while the second targeted those in Deraa, Quneitra and Damascus Countryside provinces, according to the source.
“[The] vigilance of our air defence personnel contributed to destroying large numbers of the hostile missiles and the aggression caused the injury of eight fighters, in addition to a material damage,” the source added.