"Syrian air defenses intercepted an Israeli aggression coming from Lebanese airspace," SANA said.
Earlier, state media said large explosions were heard in the Capital.
SANA quoted a military strike as saying that the strikes targeted central and southern areas of Damascus resulting in only material damage.
Military defectors said the missiles may have targeted Iranian-backed factions, particularly Lebanese Shi'ite Hezbollah that is located in the rugged border area.
Israel did not comment on the incident.
According to Reuters, Western intelligence sources said Israel’s stepped-up strikes on Syria since last year are part of a shadow war approved by the United States. The strikes are also part of an anti-Iran policy that in the last two years has undermined Iran’s extensive military power without starting a major increase in hostilities.
The intelligence sources said that Israel has over the past year expanded its targets across Syria, where thousands of Iranian-backed militias have been involved in regaining much of the territory lost by Syrian President Bashar al Assad to insurgents in the decade-old civil war.