Operations will restart at the airport at midnight, Syria's transport ministry said.
Runways at the airport were damaged in the alleged attack, rendering it out of service, according to Syrian officials.
Sites in or near the Damascus International Airport were reportedly targeted in the strikes.
Over 10 hours after the explosions were reported, Syrian state media still had not commented on the nature of the explosions.
Did the likely IDF attack on Syria prove that somehow the air force is still able to carry out all of the many security needs the country relies on it on?
Four other Syrian soldiers were also wounded in the attack.
Shrapnel from the missile fell in Rahat, southern Israel • Strikes come two weeks after last reported airstrikes in Syria
The strikes reportedly targeted a Syrian Army facility used by Iranian and Iran-backed forces south of Damascus.
The airstrike comes just months after airstrikes in Aleppo killed a Syrian soldier in April.
Jordan supported Syria's return to the Arab League but at the same time also wants the war-torn country to crack down on the drug trade.
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