"The blast was huge and could be heard in Damascus," said Rami Abdel Rahman, head of the UK-based Syrian Observatory for Human Rights.
The airport lies about 25 km (15 miles) south-east of Syria's capital.
The explosion was reportedly followed by a large fire. There are no reports of any casualties. The cause of the blast on Thursday is unclear.
Al-Manar TV, run by Lebanon's Shia militant movement Hezbollah, reports that the explosion may have been caused by an Israeli air strike. It said it had only caused material damage.