The Israeli drone attack, which was the first this year, also caused major material damage in a nearby area, the Syrian military said, but did not provide further details.
It is the second time in a year that the airport has been attacked and forced to close.
Israel has not commented on the attack.
On June 10, 2022, Israel attacked Damascus airport, causing extensive damage to the infrastructure and runways. The airport was closed for two weeks for repairs.
Israel, which in recent years is said to have carried out hundreds of attacks against the regime-controlled parts of Syria, rarely admits or comments on the attacks. However, the country has confirmed that it regularly targets Iran-backed militia groups, such as the Shiite Muslim Hezbollah, which has sent thousands of troops to support Syrian President Bashar al-Assad’s forces.