Most of the missiles fired by "Israeli military planes" were intercepted at around 11:00 pm (2100 GMT), the source said.
The Syrian military said on Friday night that "Israeli warplanes coming from the direction of the Galilee fired several missiles toward the vicinity of Damascus".
"The results of the aggression so far were limited to a strike on one of the warehouses at Damascus airport", SANA news agency cited a 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.
Only a warehouse in the Damascus International Airport was damaged, according to the statement. It claimed that Syrian air defences have foiled and countered "hostile objects" over Damascus on Friday night. That followed the September 17 downing of a Russian reconnaissance plane by Syrian forces responding to an Israeli airstrike, a friendly fire incident that stoked regional tensions.
On Christmas Day, a Syrian anti-aircraft missile flew into Israeli airspace and it was destroyed by Israeli air defenses.
Israeli Prime Minister Benjamin Netanyahu has vowed not to let Tehran - a supporter of President Assad - entrench itself militarily in the war-torn country.
An AFP correspondent in Damascus heard several loud explosions late on Friday, the worldwide news agency said.
Russian Federation is a main ally of Damascus.