Israeli missile attack also wounded four other Syrian soldiers and caused some material damage, state media says.
Citing a military source, SANA said the attack took place early on Monday.
“At 2:20am [23:20 GMT Sunday] the Israeli enemy carried out an air attack from the direction of the occupied Syrian Golan, targeting areas in the vicinity of Damascus,” it said.
The attack killed “four soldiers and wounded four others”, it said.
The agency also reported “some material damage” and said that Syrian air defences had intercepted some of the Israeli missiles.
There was no immediate comment from Israel.
Israel has for years been carrying out attacks against what it has described as Iran-linked targets in Syria.
Tehran’s Iran’s influence has grown in Syria since it began supporting President Bashar al-Assad in the civil war that started in 2011.