State news agency SANA said two shells were fired at the Russian embassy, one hitting the compound while the other fell nearby. SANA said the shelling of other parts of the city wounded seven people.
Syrian rebels in the suburbs of the capital have previously struck the Russian embassy. The shelling came as government forces have been pounding rebel-held areas near Damascus for days.
Moscow is a strong supporter of President Bashar Assad and has been involved in Syria's civil war since September 2015.
The group, which tracks the civil war through a network of on-the-ground activists, says it has documented 331,765 deaths by name while the rest have not been identified.
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The attack in Damascus came hours after a bomb exploded near a hospital in the rebel-held northwestern city of Idlib, wounding five people.
The Syrian Civil Defense group, more popularly known as the White Helmets, said the wounded included two children. The Observatory said five were wounded including children.
Explosions have killed thousands of people in Syria since the conflict began in March 2011 with anti-government protests before turning into a full-blown civil war.