According to the Russian Foreign Ministry, a mortar shelling hit hit the fence of the Russian Embassy close to a building of its residential quarter, causing damages to power transmission lines and water supply system.
None of the staff in the embassy were injured, the ministry added.
Noting that the embassy was purposefully targeted, the ministry also called upon the United Nations Security Council to condemn the "brazen action".
The Russian embassy in Damascus has been shelled several times since Moscow started to participate in anti-terrorism operations in Syria in September 2015.
The Russian air force is currently providing support to the advancing Syrian government troops in the east of the country against Islamic State (IS) terrorists.
Dozens of strikes have been launched by Russian bombers and submarines near Abu Kamal, one of the last IS strongholds in Syria, since the beginning of November.