Syria’s al-Ikhbariya Television said the explosion "resulted from a terrorist attempt to target the Mezzeh military airport".
The blast came when an explosive-laden car went off outside the base, causing a massive fire in a nearby gas station, Al Alam reported Sunday.
There are conflicting reports about the number of casualties but some sources say at least 20 soldiers were killed in the attack.
The Syrian crisis began in March 2011, and many people, including large numbers of government forces, have been killed.
Damascus says the chaos is being orchestrated from outside the country, and there are reports that a very large number of the militants are foreign nationals.
The Syrian government says the West and its regional allies -- especially Qatar, Saudi Arabia, and Turkey -- are supporting the militants.
In addition, several international human rights organizations say the militants operating in Syria have committed war crimes.