The Israeli Air Force also targeted two tanks of the "Syrian regime" in the northern part of the Golan, the spokesman said, adding the projectiles did not cause any casualties.
"Because of the unacceptable violation of Israeli sovereignty", Israel has protested to the United Nations Disengagement Observer Force (UNDOF) which monitors a 1974 ceasefire between the two countries, he added.
Israel has conducted multiple air strikes in Syria since that country's civil war erupted in 2011, most of which it has said targeted arms convoys or warehouses of its Lebanese arch-foe Hezbollah, which is a key supporter of the Syrian regime.
Israel did not confirm or deny the reported Damascus attack.
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Israel seized 1,200 square kilometres (460 square miles) of the Golan from Syria in the Six-Day War of 1967 and later annexed it in a move never recognised by the international community.
Around 510 square kilometres of the Golan are under Syrian control.
The Israeli side of the Golan Heights has been hit sporadically by what is thought to be stray fire from fighting between forces loyal to Syria's government and rebels.