State news agency SANA said two shells were fired at the Russian embassy on Sunday, one hitting the compound while the other fell nearby.
Syrian rebels in the suburbs of the capital have previously struck the Russian embassy.
Moscow is a strong supporter of President Bashar Assad and has been involved in the six-year war since September 2015.
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 Britain-based Syrian Observatory for Human Rights also said five were wounded including children.