Citing a military source, SANA said "terrorist groups" fired shells from neighbourhoods east of Damascus, but it did not report any casualties.
It was the first reported attack on the capital since a ceasefire began at midnight.
A security source in the capital told AFP that there were no casualties when about 10 shells hit the Abbasiyeen neighbourhood.
A resident confirmed that shells had struck the district in the late morning.
Syria's armed forces issued a statement warning against "the consequences of such actions" and called on civilians to remain committed to "local reconciliation".
It appeared to play down the attack, saying the army "was confident that most citizens are eager" to avoid an eruption in hostilities.
The Syrian Observatory for Human Rights monitoring group said it did not record any attacks on central Damascus today.
Tensions are high as rebels have also accused the government of intermittent "truce violations" in parts of the country today.
The ceasefire does not include jihadist groups.
