The attack early on Monday, the second in seven months to put the Damascus International Airport out of service, caused material damage in a nearby area, the army said, without giving further details.
Israel has targeted airports and ports in government-held parts of Syria in an apparent attempt to prevent arms shipments from Iran to militant groups backed by Tehran, including Lebanon's Hezbollah.
An opposition war monitor reported the Israeli strikes hit the airport as well as an arms depot close to the facility south of Damascus. The Britain-based Syrian Observatory for Human Rights said four people were killed in the strike.
There was no comment from Israel.
On June 10, Israeli airstrikes that struck Damascus International Airport caused significant damage to infrastructure and runways. It reopened two weeks later after repairs.
In September, Israeli airstrikes hit the international airport of the northern city of Aleppo, Syria's largest and once commercial centre, also putting it out of service for days.
In late 2021, Israeli warplanes fired missiles that struck the port of Latakia hitting containers and igniting a huge fire.
Israel has carried out hundreds of strikes on targets inside government-controlled parts of Syria in recent years, but rarely acknowledges or discusses such operations.
Israel has acknowledged, however, that it targets bases of Iran-allied militant groups, such as Lebanon's Hezbollah, which has sent thousands of fighters to support Syrian President Bashar Assad's forces.
Thousands of Iran-backed fighters have joined Syria's 11-year civil war and helped tip the balance of power in Assad's favour.
Israel says an Iranian presence on its northern frontier is a red line that justifies its strikes on facilities and weapons inside Syria.
