Government forces were also battling rebels in the city's outskirts including the eastern suburb of Mleiha, where government war planes carried out air strikes during heavy fighting with insurgents on Sunday.
"Two citizens were martyred and eight others wounded by mortars fired by terrorists at the opera house ... in Damascus," a report on state news agency SANA said on Sunday.
It did not say exactly when the attack occurred.
President Bashar al-Assad's forces are in control of central Damascus but rebels have been able to launch mortar and rocket attacks into the city's centre, sometimes hitting heavily-secured weathy districts and embassy grounds.
On Saturday, the Syrian Observatory for Human Rights, the British-based monitoring group, said a mortar round fell near the Russian embassy in central Damascus, and two more rounds landed near a security building. No casualties were reported.